As someone said time of year is important, most mountain passes are pretty clear after April/May time frame but sometimes mother nature will fool you, I have seen a freak snow storm in Wyoming in early June, snow one day , 70 degrees the next Ugh .....
But one thing that you will come across out west is mountain grades an passes with 40 percent grades for 10, 15 or more miles, some with switch backs so make sure your brakes are up to par.
The best advice I can give someone who has never driven out here is pay attention to the road signs out here in the mountains passes, take your time going up and down the passes, " DO NOT STAY ON YOUR BRAKES ", if you have an engine brake or what some manufacturers call a tow function use it.
I can't say it enough STAY OFF YOUR BRAKES only use them when needed to keep you at a slower speed. When coming off a pass (Going Down) start off slow and stay that way till the last mile or so. Do not believe these cowboys who say they can go over passes at 60mph, maybe they have a trailer that weights 4,5,6000pds but even they scare me. You will see signs that say run away ramp X amount of miles ahead, these ramps are not only for 18 wheels but people who loose their brakes because they have got so hot they stop working .....:E