I would do carpet as well.

We live in a rental that has floor boards throughout and no insulation! It is colder in our house than outside. There are drafts everywhere. Yes the floorboards look lovely but carpet would be much nicer underfoot and act as an insulator.

Just get some cheap carpet (that wont show alot of stains and make sure you state in your lease agreements that carpets must be professionally steam cleaned at end of lease and receipt shown or something like that.