I did this drive dozens of times in college. One of your main goals should be to avoid Longmont, which is one of the scariest agglomerations of suburban hell in the world.

Take the diagonal to CO-52 and take that to I-25. Take 25 N to the CO-14 exit into Ft. Collins. You can then jump US-287 N to Laramie.

I've driven this route in all kinds of weather and it isn't overly bad, as the highway doesn't get much above 7500'. I will second the earlier point about speeding, however, as I did get dinged for 75 in a 55 (It should be 65 now) just before Virginia Dare. Don't let the isolation fool you, our buddies in the CHP are out there waiting to ruin your day.

Running 80 over to 25 into Cheyenne isn't really any better, as you have to go over 8000' on 80 where the weather usually turns nasty. I'd much rather take my chances on 287.