Yes, housing policies differ at each college. It will always be very explicit what the policies are, although you may have to hunt around to see where it is listed on the actual college website, or even contact housing to find out. When you sign up for housing, you will sign a contract that has the details on whether students can stay during breaks or not. On some campuses, international students are allowed to stay, or students in specific buildings/types of housing are allowed to stay. It can also vary by which break it involves – winter break between semesters, spring break, holidays, etc. Typically most students are required to leave college housing during winter break – they can leave their stuff in the room, but just not be there themselves. Some smaller colleges may require all students to leave during breaks. It might be helpful if you made a chart with this information as you gather it, so you can compare the offerings of the different colleges since this will be an important consideration for you.
When thinking about your college location, you should also consider transportation issues. The U.S. is very different from Europe in that regard. Look for locations with lots of public transportation, nearby restaurants and shops, bike lanes, etc., so you are not stuck on campus with nothing to do and nowhere to go without a car. It is not a given that communities here have public transportation or walkable areas like in Europe. Many colleges are very isolated, with a car being almost a necessity.