Those winds the other day were not a seasonal-typical thing, but a very strong backdoor cold front, its strength being unusual even for here. Agree with others that indicate that going north thru Utah is usually preferable to crossing Wyoming on 80, which is always windy (and sometimes dangerously so).
Watch out for TRAFFIC between Provo and Ogden, UT. By the time you get to Brigham City, it thins out enough to be tolerable again. :)
In October some of the areas you are going in central Idaho can get wintery - just keep on top of the weather forecasts as much as possible and wait it out if you need to. Be aware that a lot of campgrounds close down or go to very limited service after about October 10, certainly after the 15th, so be sure you have some alternates in mind. Good luck & safe travels!