My experience with weather. I have killed most of my deer on moderatly cold days, usually before 11 AM when it is sunny, bright and absolutely dead calm when I am hunting from a stand. I find that you can find deer in a snowstorm but you have to move, sitting in the usual places doesn't seem to be productive and I believe once the snow is coming down in big fat slow lazy flakes the deer will look for some shelter and lie down (generally) and some are just slow getting there and you can cut a trail if you're moving. Evenings can be productive but mostly I see does and fawns as the light fades, I think (generally) the bucks hang back a little more in the evenings as they move to feed.
Really really cold weather I have found not to be very productive as deer seem to hunker down and then move after dark (in my experience) -10 to -20 seems to be optimal, but there are always exceptions. The biggest deer I ever saw was at -30 in early Jan walking down the middle of a frozen river in the bright sunshine, he was gorgeous and one of the most beautiful things I ever witnessed
Rain (in my experience) is a crap shoot but deer will move in the rain, they really have no alternative because they live outside and it rains all the time so they deal with it, but you as a hunter are going to be miserable and probably less attentive in a bitter cold November rain, so by extension you are probably not going to see as many deer. I have found though that one of the absolute best times for deer movement is immediatly after the rain stops and the sun comes out. They seem to want to just get up and walk around in the sun, but it is only for a short time after the rain stops and you have to be out there in the rain to be there when it stops, if you wait in the camp for the rain to stop and then go out, you missed it (in my experience)
Just a few musings from my 45 years chasing whitetails in New Brunswick, Nova Scotia, Sask and Alberta. I keep a diary of everyday in the woods, weather, temp, where I was,who I was with and what we saw. its fun to look back over the years and it doesn't take long for some patternss to start to emerge.