If you need A LOT of financial aid, then you need to follow the money, not follow the weather. Beggers can’t be choosers.
I agree with others that it as important as you make it. It goes along with urban or rural, large vs. small etc. if you’re sensitive to Seasonal Affective Disorder then being further south might not be a bad thing. For some the change in seasons give them an opportunity to change focus. Winter is a time to cacoon, spring a time of rebirth and feeling new, summer taking it easier and being more casual and autumn well autumn (and least to me) is just plain awesome. The downside is that there are fewer “ideal” days and for some reason they often seem to land when you can’t appreciate them. If being warm and dry is important to you then the southwest seems a better idea than the rest of the country. Your question is a good one to get an answer to but the only one who can give a meaningful answer is you.
@GMTplus7 Financial aid will not be a concern. I might also get national merit money.
@myjanda Interesting. My mom is encouraging me to look at schools in Boston because we have family friends there and she loved when we lived there. However, coming from one of the least humid places in the country, I think I’ll find New England summers downright balmy 
A couple of you have mentioned the PNW. There aren’t any schools in that region that I’m particularly interested in, but it seems beautiful there. I don’t think I could handle the constant grayness though.
When you graduate college, do you see yourself going back to Arizona? Your best job options may be closer to where you go to school. I’m all for picking a school that has what is important to you, including weather.
My daughter is moving to Boston from Hawaii to start college this fall. She has no idea what winter is. Wish her luck! 
Weather should be a factor. But among all the factors, it should be way down the list. It won’t even crack top ten in my case.
Remember, even in cooler locales, there are still plenty of nice weather days in Fall/Spring.
One tip, if you can learn some outdoor winter activities like skiing, fat biking, xc skiing, snowshoe, ice skating, etc. it can make winter fun at times.
I went to college in the south. I liked the weather a lot. When I moved back to New England it took me a while to adapt to winter and i was depressed. That was until I learned to snowboard and I’ve never looked back. I actually look forward to winters.