Deer have to move when they do, to get where they want to go. They of course use wind currents to smell for danger, but I doubt it's normally a primary reason they go the direction they are going.
I like dead calm, and better yet a light, predictable wind direction. With that one can plan hunt specifics. To some deer hunting is always done from a stand or blind. They may say 'you can't walk up on a deer in the woods'. Even a stand location for that hunt the wind comes into play. I never want my scent drifting into the best cover I hope to see deer come out of.
I like to hunt into the wind, or at least some version of a crosswind. It helps to have some elevation where able. Much of the time while 'still hunting' you are still, posted up, standing or sitting. That's the main time you see a deer come into view.