When this happens you end up with low-frequency rumbling in the resultant audio channels. Although with some amount of low-frequency rumbling can be removed in post with audio filtering programs, the result is usually not very satisfactory.
The problem is most likely to happen with one of the smaller "palmcorders" or a digital still camera that also has a video mode.
I was recently shooting some thunderstorm activity on nearby Mt Lemmon with a camera mounted on the window of the ClamCamVideoMobile. Although it wasn't particularly windy there were light breezes.
When I returned home and played the video I found it was filled with that dreaded rumble that pretty well ruined the great thunderclaps that were also recorded.
I decided to try a wind-protection "trick" on two of my cameras - the Sony HXR-MC50 (using its built-in mike) and the Sony RX100 still camera that has a video mode.
Two photos below show the microphone ports on the two cameras. I decided to try covering them with some open foam about a quarter of an inch thick.
After carefully gluing the foam pieces on the cameras using Elmer'r rubber cement, they look like this.
Here's some audio from both cameras with and without the foam applied. The background noise that you hear is the fan that's providing the "wind" for the test.
The foam on the MC50 obviously to do a better job than that on the RX100, even though there is some wind noise reduction for the RX100. I attribute this to the fact that there wasn't enough room on the RX100 to cover much beyond mike port's themselves. I may try a larger, thicker, piece of foam on the RX100.
There was no attempt to capture the audio of the participants but you can hear an orchestra in the background without the severe wind noise that would have been present if the foam had not been applied.
TO FIND OUT CURRENT WIND CONDITIONS IN THE USA GO HERE.