I've had some great hunts in very windy weather.
I hunt what I call "pockets", which include anywhere there's a break from the wind. In mountainous country, that includes the brushy "headers" where side draws top out on ridges on the side opposite of where the wind is coming from.
Strong winds are generally consistent, rather than swirling, and the noise from the wind helps cover small noises I may inadvertently make while stalking.
Incidentally, some of my closest shots at deer were on just such days.