Last year, in our 300 hp DP, we ran from Missoula, MT to Gillette, WY, late in August, on I-90 and had no real issues. Jim's right about the part east of Butte which is an interesting piece of Interstate, but speed management is the key to handling the grades, both up and down.
One of the rules of thumb we used as we got used to our coach in the mountains of the west was to use the speed warnings signs as gospel on the downhills. If it said 45 mph, we wanted to be at 45 mph, and steady, not increasing speed. We found that concept to be comfortable, reasonable, and there was never a feeling that we were on the edge of being out of control. My wife drove as much or more than I and she found that worked for her as well.
If you are not real confident, avoid getting in a pack of traffic and maintain some extra distances between you and the other traffic. That's not real hard in some of the remote areas of Wyoming!
Proper use of your engine brake will also go a long way towards helping you find your comfort level.
There are several posts in the Forum about mountain driving techniques and those will give you some good tips as well.
Take your time and enjoy the scenery! Everyone who has done it had a first time.