You will have a problem with the winds on the high plains, particularly just east of the Front Range, only if you try to drive in them.
High winds are not continuous, they come up as weather systems move across the continent. When it is too windy, you sit it out, when it is not too windy, you go. There is not a good or bad time of the year, except that in the southern part of the plains, Summer tends to be calmer more often.
Where I encounter the winds: Kansas, Oklahoma, west Texas, eastern New Mexico and eastern Colorado, they are more often from either north or south, thus crosswind for east-west travel.
If winds are forecast much over 30 mph steady, I may or may not go in a car, definitely won't go in the RV. 15-25 mph crosswind is close to my limit for maintaining control of my C at highway speeds, so they slow me down. One of my friends lost a trailer (flipped) to a 30 mph gust.
Winds over 45 mph (often meaning 60+ gusts) I won't even go out on foot. Trees shed limbs, sometimes uproot, at those wind speeds, in this part of the country.