If so, is it guaranteed? I read on their website that residence is assigned on a first-come first-serve basis, so if you apply for housing really early, will you be able to get housing for all 4 years? Or do they only offer it to freshmen and sophomores? I can’t seem to find this on their website or anywhere online. Thanks!
Housing is guaranteed for 4 years.
Although if you want to be picky of where you live… the lottery starts 
Hope that answered your question though ^^
Don’t be scared to apply. It’s a great school (arguably one of best in the world) in the best city~~
On-campus Housing is guaranteed at Columbia for 4 years, for traditional undergrads at CC and SEAS.
It is not first come first serve. Your choice after the first year are dependent on your Lottery number, which is stratified according to your year. Of course, if you were to miss the deadline for registering for the lottery, then you would be out of luck.
Also, just about everyone lives on campus because it is so darn expensive to live off campus (close by and in safe neighborhood). So you have to adhere to the Housing policies. There are actions which could cause you to lose your guaranteed housing, and other actions which could get you kicked out of housing, but without getting you expelled from school. Unless you are well-to-do, the first 2 would be just about as bad as the last.
As for other programs: Housing may or may not be guaranteed for all 5 years, for some of the 5 year program. But this depends on the program, so that has to be checked according to the individual plan.
If you are looking at something on the Columbia website that refers to first come, first serve, then you may be looking at University Apartment Housing, which is completely different from the undergrad University Residence Halls. UAH provides more apartment type residences for graduate students and nontraditional students (including General Studies). UAH does Not guarantee housing for anyone, although prioritizes according to PhD doctoral candidates and timeliness of the application.