There are a couple of main factors. First, in any place on the planet, the higher up you go- in general the stronger the winds are. This is because the higher up you go, the less of an effect the earths surface has in creating friction and slowing the winds down. So winds are typically higher in ANY mountain range than they are at the lower elevations.
The Medicine Bow Range, which the snowies are part of, is unique in that it is surrounded on the west, north and east by relatively flat and treeless terrain. That allows the wind speeds to be a little higher than average when compared to other areas out west. Also, much of the snowies are more like an elevated plateau than a large mountain range, with lots of large peaks- which also tends to allow wind speeds to be a little higher than in other mountainous areas.
So the wind speeds are greater there than in some other mountainous riding areas, but folks heading out to ride anywhere out west should also be prepared for stronger winds than they see while riding most Midwest locations.
The winds are in general a little weaker in the summer due to the fact that wind speeds in the summer are lower in general during the summer than they are in the winter at the higher altitudes.
-John