Since you haven’t been able to visit these three universities, let me describe the biggest difference in terms of campus and location.
UMinn Twin Cities is in Minneapolis-Saint Paul, which has 3.5 million people. You can see the skyline of Minneapolis from most parts of the main campus, which is gorgeous and right on the Mississippi River. The light rail stops right on campus, and you can take that to downtown Minneapolis or downtown Saint Paul,and also to the international airport and Mall of America. There are also buses that can take you everywhere. Minneapolis is also top-rated for bicycles with lots of bike lanes, so some people ride their bikes everywhere. Whatever interests you might want to pursue off-campus, you can find it in Twin Cities. As for the cold winters, UMinn has that covered. There are tunnels across each campus, and you can take those if it feels too cold for you to walk outside. Housing includes apartment options on campus and near campus, even for freshmen. One apartment building is even connected to the student center by tunnel, so you could walk over there and eat without ever putting on a jacket. The tunnel on campus is called the Gopher Way. (That said, my daughter has been at UMinn for two years now, and has yet to feel cold enough to use the Gopher Way, and she grew up in the South.) Downtown Minneapolis and Saint Paul have skyways, which are like the tunnels only above ground, connecting buildings. The light rail stations and bus stops also have heat lamps to stand under to stay warm.
UW Madison is in the heart of a city of half a million people, so you can walk to lots of restaurants and shops. It is the capital of Wisconsin (like Saint Paul is for MN), so it is a vibrant city. Although this is a smaller city than Twin Cities, the campus might feel more urban because it is not a separate green campus like UMinn but rather is right there surrounded by Madison. Lakes are adjacent to campus. As for it being liberal, nothing in the Midwest is more liberal than SoCal where you are from, so I wouldn’t worry about that.
UIUC, by comparison to the above two universities, is in the middle of nowhere. Urbana-Champaign metro area has a quarter of a million people, but it really feels like a small town next to a very large campus on flat terrain, with nothing else in the area except farm land. I’m originally from Florida and have been to UIUC in the winter, and I can tell you – UIUC is cold! It might feel every bit as cold to you as the other two universities, only it won’t have the Gopher Way tunnels of UMinn, or the buildings all around to step inside if you’re cold like UW. Keep in mind that the other two locations are not extremely cold every day in the winter. There are cold fronts that come and go, and also much of the cold weather happens during winter break when you will likely be back in SoCal anyway.
You mentioned that ChemE at UIUC is not in the College of Engineering. I think this is a big deal. Your university experience will be strongly influenced by the college you are in. I can’t vouch for all of the universities, but at UMinn where my daughter attends, the college affects everything, such as: type and frequency of advising for your classes and major; procedures for scheduling advisor meetings and switching majors and declaring a minor and all other procedures; policies for selection for dean’s list; method and frequency of communication for updates on activities and opportunities including internships, research positions with professors, alumni meetings, job fairs and more; special events and speakers; college affiliated clubs and leadership positions; housing communities for specific colleges and majors; etc. In addition to these issues, each college typically has a different set of core courses, and that can vary quite a bit. If you think you might change from ChemE to another engineering major at UIUC, it might be harder for you to switch into the engineering college, or you might have to wait till you have taken a certain number of courses. You should check on all of these things if you are considering UIUC.
All three are great universities, part of the Big 10, and with strong reputations overall and for engineering. You really can’t go wrong with any of them.