You might want to check out Case Western - not near skiing - but it doesn’t require a separate admit for its engineering programs. So he could do chem or chem e and doesn’t have to decide until later. If his ACT/SAT comes in as anticipated, CWRU can be generous with merit scholarships. Demonstrated interest is important.
A home schooled child or one at a small private school is purposefully in a small intimate school environment through their elementary, middle and high school years.
After the purposeful choice for a low student - faculty ratio, why then navigate the college search into the total opposite end of the spectrum? Why pick a large OOS public college?
Why not a small private college?
Where did you get the idea that homeschoolers choose to homeschool so their children are in a “small, intimate school environment,” ClarinetDad16? The whole point of homeschooling is to open the world up to our children, not keep it out.
I run a network of several hundred homeschooling families. Our group travels regularly (in state and out of state) for classes and activities that interest us. Many homeschoolers in our network enroll in a local college for their last two years of high school, so by the time they earn their high school equivalency they’re well traveled and used to navigating college. After spending so much time learning with all types of families in all kinds of places, why wouldn’t they consider attending a large OOS college?
@mmom99, Some of the SUNY schools are near good skiing. I think their OOS rates are ~$30k/year. New Paltz, in particular, is pretty outdoorsy. They’re near skiing, Minnewaska State Park, and the Walkway over the Hudson. If your son gets bored with the country, he can take the train into Manhattan.
Uvermont ?
An issue with ChemE is that it suffers from extreme grade deflation. Employers know that a 3.0 is really good, but Med schools don’t care.
UMinnesota is topnotch for chemistry /chemE.
So for the homeschool kids in your network what is their typical student / faculty ratio during high school?
@ClarinetDad16, Why does it matter?
I don’t want to derail OP’s thread. There are plenty of books available about homeschooling. If you truly want to understand it better, try reading up on it. My point is that there’s no reason for OP’s child, or any student, to limit themselves to a particular type of college based on the type of high school they attended. If OP’s child wants to attend a large OOS college, the only reason he needs is because that’s what and his parents want.
CU Boulder is not part of the WUE and not generally known for generous though with the right stats, they may be. Colorado State, Montana State, U of Montana, Montana Tech and U of Wyoming would all be good, especially Colorado State in my opinion for great deals. WUE is irrelevant though since OP is not in a WUE state. That said, their OOS merit offerings are good across the board. Ski bus from campus. Mechanical is impacted but I think that is it. Absolutely outstanding for outdoor activities, Fort Collins is a wonderful town, nice honors program and a very solid school.
@ClarinetDad16 You’re basing your questions on the assumption that all homeschoolers choose it for small class size, when small class size is often just the by-product (of choosing it for the options in curriculum).
Have you run the NPC for the ivies? If so, and if the result is nowhere close to your $25-30k target, why apply “for funsies”? It seems like that just perpetuates the problem of application inflation going on at top schools, wastes the school’s time, and potentially takes an acceptance away from a student who is really interested in going there.
University of Vermont sounds like a perfect fit for him except that it doesn’t have Chem E. It does have other accredited engineering majors, however, and Chemistry. Take a look at it. Beautiful campus with nice people. Good music scene–will be easy to make friends doing it casually. Fantastic college town near skiing and pretty generous with scholarships. Worth checking out considering the Chem E is your suggestion and not (doesn’t seem to be based on your write-up) his burning desire. It’s a good springboard to medical school.
^ why decide now however? ChemE is basically nixing Med school, due to the infinitesimal odds of making it from that major to led school. He could apply to Lehigh and Trinity and umn and uvt… And in a year, the boy may have a clearer idea for a career path : physician or engineer?
@flatKansas and to that point what if the OP searched for the best fit college curriculum, which as a by product also had a small class size?
My oldest son had not as good stats but applied to ChemE schools four years ago. Here’s my additions:
University of Utah is worth another look. The city has been attracting people from all backgrounds, and the college, with generous merit scholarships, has also. It is much more cosmopolitan than even 10 years ago. It is probably the 2nd best college for skiers in the US (after Montana State, but don’t go there). If he stays over the summer tuition becomes in-state.
University of Wyoming is a bargain, but would be heavily conservative christian, maybe not his top choice for environments. Also, the skiing is not great unless he is willing to schlep down into Colorado on snowy days, not best for a kid trying for med school.
One college that offered my son a big merit scholarship is University of Dayton. A friend’s son is there now, still doing robotics and studying EE. It routinely ranks as some of the happiest students.
Texas A&M has good guaranteed scholarships for NMSF (read the requirements). UT-A and UT-D are also luring top students with merit scholarships. Skiing in Texas is non-existent but, realistically, I was a big skier in HS, stayed in the NE, but only went maybe 10 times while I was in college.
I guess it depends, but I gotta believe Chem E is way harder than a straight Chem degree pretty much anywhere. I will admit, though, that I dropped Organic Chem and Chem E at the same time. 
A typical chemE GPA may be 2.7 with 3.0-3.2 being very good. In chemistry or CS, a typical GPA may be 3.2-3.3, with a 3.7 very good. Obviously I’m not talking about Brown, which is premed heaven with average GPAs around 3.6 so that most good students have med school worthy GPA 's.
Med schools often want 3.6 from unhooked applicants and they don’t say ‘but this is engineering, a 3.2 I’d like a 3.6 in another major’, engineering students must meet the same criteria as others.
So, engineering is a trade off - better access to professional jobs after college but fewer odds of making it to Med school.
http://www.gradeinflation.com/ includes a table indicating that GPA in engineering is higher (by about 0.2) than GPA in natural sciences. Social science GPAs are similar to engineering GPAs, while humanities GPAs are higher. Of course, specific schools and departments may vary from the overall average.
But it does mean that the common assumption that “engineering is worse for GPA than science” is not necessarily true. Of course, if a science or other major pre-med has more free electives to cherry-pick “easy A” courses for GPA-raising purposes, that may help (though there are still the pre-med science courses and science GPA that pre-meds need).
My parents made me do the research for colleges and then do a presentation to them. While I was not happy doing it, during the first couple schools I enjoyed it and learned more about what I wanted to study, different colleges in Universities, what attracted or disliked in a University.
College Board and edu.gov is a great resource. Started with 30 colleges and now down to 12.
Parents let your child do their own work. Then support and ask the What, When, Why questions.
My dad is taking me on a 12 day 8 school visit starting Thursday and than 2nd week in August my mom is taking me on a 6 day 4 school visit.
My goal is to apply to 4 and my final decision will be based on $$, honors college, campus, and ease of airport access (if 2 schools are tied).
Apply to more than 4, unless you can afford to be full pay everywhere. Many students shortchange themselves financially if they apply to only 4 schools.
@ucbalumnus : I don’t know a single school where engineering is easier in terms of grading. Zero. Engineering is hard, has lots of required classes, is sequential, and takes pride in its severity complex. 
In addition, that’s not how I read the small paragraph in the paper you linked to. The author makes no claim about biological sciences being easier graders than engineering, and simply states humanities are the most generous, social sciences are in the middle, and hard sciences are the least generous.
@ClarinetDad16 You might want to stop trying to stereotype home educated students as cloistered, socially inept people. Who cares if they learned in a small environment? They used the benefits that environment had to offer and would like to try something new. Your comments only show your baseless disgust for home education, nothing else.
In addition to How, What and Why, the big question is usually How Much?!
Good luck.