Hopefully there won't be much ice and no one will have to worry about it, but last year we tried the whole front wheel drive thing up the mountain and ended up sliding backward down hill with trucks waiting below for us to get out of the way. When it's just a road, not a big deal, but when it's a narrow road with a mountain on one side and a 300 foot drop on the other, I don't like to take chances. Of course, depending on where you go, what resort you want to go to and which way you get there, you may not have to deal with it at all.
As far as your drive from FAT to SLC, I always use
www.mapquest.com to get driving directions and time estimates.