The basement would be fine, but the room would need several changes of air per hour, which would have to be preheated and humidified in another room (cellar?) to maintain a steady temp during the winter. you could always use the warm air from the rest of the house if you ran it through a filter first, the only problem might be the O2 content. You could probably get round that by adding a few drops of hydrogen peroxide to the mister water.
There are a few varieties from japan and Europe that will even grow in snow. The ones in the pic are warm weather pleurotus columbinus. If you've got mushrooms growing in the woods near by, you could always clone them...
Its a good thing to get into. I've got people pestering me for mushrooms already. The guy at one of the local Chinese restaurants keeps asking me when they're gonna be ready, and my friend who works at another says they'll trade mushrooms for my favourite food .lol. I'll never cook again.