Forget about it
MTB is out of the question unless you are into walking through ankel deep slush. There are no trails that can be ridden right now. You can try to ride the shoreline but will do lots of walking through the snow and mud. Any riding that can be done will not resemble what I think of as mountain biking. (where I get to pedal and don't have to stop every 10 min).
Road riding is possible if you are desended from a penguin, and want all the benifits of smoking a pack of cigerettes without spending 5 bucks. Bottom line. The snow sucks the air sucks, the winter sucks, SLC sucks, and leave your bike at home until june. In june there is some OK riding in the lower elevations, and by august the snow melts off the mountans enough that you can ride really good trails until oct when it snows again. Do yourself a favor and stay away from SLC this time of yeat. its one of the worst places in the nation to be.