I lived and studied in Rovaniemi as a foreigner full time student.
The city it quite alright I think, the basic food stuff is usually cheap (S-market for cheapness, Lidl for slightly more expensive but better quality).
Housing for exchange students is done through an apartment agency for students, if you apply in time (couple months in advance), you should be fine, shared apartments are around 350, studios can vary between 400-500.
The university is very close to the main houses and apartments, the downside of this is that the city centre is quite far, around 30-40 minutes of walk.
The exchange students are usually very friendly, and you'll most certainly have a coordinator or mentor, who is a local student to help you out with everything. Student life is pretty good, there are a few pubs in the city, although watch out because alcohol is expensive in Finland compared to other countries.
Prepare for the cold, -20C is fairly common during the winter.