I'm sure I've mentioned this many, many times (probably every time this topic comes up), but we keep extremely detail records of everything when we're hunting, and have for 35 years. Looking at wind speed and bucks seen while hunting (buck sighting rate [bucks seen per hunting hour]), as wind speed increases, buck sighting rates decline. Basically, the higher the wind speed, the fewer bucks seen. However, there is one interesting caveat, and that is extremely strong winds, the type of winds where it's frightening to be in a stand. In these conditions, buck sighting jump up dramatically. Yet looking at individual cases indicates these bucks are seen running through the woods, not walking or going about their daily routine. I strongly suspect these wild wind conditions, and all the violent motion in the habitat, spooks deer and makes them very jumpy, hence the observations of deer running.
When asked why increasing wind speeds would reduce buck movement, I'm not sure that is actually the case. I also suspect this is just a product of motion in the habitat. When the winds are dead calm, the human eye is quickly drawn to any movement of a deer through the woods. Yet when winds increase and all of the branches and leaves are moving, subtle motion of a deer slowly slipping through the woods is not noticed. So it may be that increasing wind speed does not alter deer movement, but it does alter the human eye's ability to detect it, hence reducing sightings.