I'm not sure about others, by my basement is actually warmer in the winter and cooler in the summer than my own bedroom, so my pigs live down there - and when I have visitors they sleep in the "guest bedroom" I have set up down there. This may not be the case in an "unfinished basement". I have not experienced any drafts, they aren't really near any windows or anything, the only downside is they don't get hardly any natural light so I have to leave the lights on down there a long time. I'd try hanging out in your basement for a while - see if it's comfortable for you. If the climate feels just as well as the main floor, the pigs should be fine. If you're cold, they will be cold too. The unfinished basement in my old house was way too cold for pets so I imagine it varies.
(Added) Also, consider how much foot traffic you have in the basement. I go down there a lot - my craft/sewing/scrapbook area is connected to the pig's room and so is my laundry room and storage, so I'm walking by their cage regularly. I think pigs are much happier when they are in a central location where they can see you frequently. At least my pigs seem to feel that way.
