When you are in Wyoming, you should consider attending the Wyoming Wind Festival.
It runs from Jan 1 to Dec 31.

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That said, I've lived and toured in Wyoming for 20+ years - all areas, all seasons.
One thing for sure - you can count on wind - but there is little predictable about it.

Overall, prevailing summer winds in Wyoming are SSW west of the Continental Divide and SSE east of it.
In Yellowstone, winds are generally less of a problem because of forest cover - generally NW.
In Jackson Hole, Prevailing winds are southerly.
From Togwotee Pass to Muddy Gap winds are westerly and often strong.
From Muddy Gap to Colorado winds are SSW.

So if you are heading to Colorado, you are likely (not guaranteed) to have headwinds in Jackson Hole, north of Rawlins, and south of Wolcott Jct - but should have tailwinds in the toughest stretch - between Togwotee and Muddy Gap.

If you are heading from Colorado, you are likely (not guaranteed) to have side to tailwinds as you head north, but strong headwinds heading west through Lander and Dubois. YMMV.

As a general rule, winds are lightest in the morning and strongest in the late afternoon. The best cycing time when anticipating headwinds is as early in the morning as possible. (Plus it's the coolest) Sometimes there is a little let-up in the evening before sunset - but not always.

Prevailing winds means "prevailing".
On any one day they may be coming from the opposite direction.
Such is wind.