vail to steamboat. head west on US40 to craig, co. from craig head north thru baggs, wy to I-80. go west on I-80 to rock springs, wy. go north from rock springs to jackson. (sorry i don't know the other roads off the top of my head, you can find them easy on google maps)
the road through baggs can be bad if it is snowy. i drove it just before thanksgiving and i literally couldn't see more than 2 feet in front of my truck and was traveling at about 20 mph. then maybe the part coming into jackson could be bad if it is snowy. none of the roads are gnarly, mountain passes. just some state, two lane roads mostly. if it is snowy out just slow down, turn on 4wd, and pay attention. you'll be fine.
if you have any other questions, let me know, i have done that drive a lot and am very familiar with it.