I hunt the entire day, an hour before sunrise until its dark.
I see more deer movement in the mornings and more bucks. Towards evening I see far more does and fawns. As deermanok has suggested, from about 10 until 2 has shown me a lot of deer and interestingly I see far more quality bucks during this timeframe. I'm a meat hunter and use almost the entire animal for making sausage, the exception being the back loins which I cut into chops.
I don't pay much attention to moon phases except that during the new moon period, two days prior and two days following, I see deer active later into the morning and earlier in the evening by about a half hour each way. Fog, drizzle, light rain and light snow I welcome as deer activity seems to increase.
Like ninering's dilemma with heat, our last couple seasons have been unusually warm and the need to get things chilled quickly has offered some challenges. When I was early into deer hunting back in the 60's hunting in November weas a COLD proposition, often with a lot of snow and wind to accompany the cold. I'm talking below zero cold. In the last twenty years I think I can count on my ten fingers how many times I have had measurable snow on the ground or snow that stayed for more than a day. A couple years ago I sat out a wicked thunderstorm in the stand until the rain went sideways. I was soaked. I started off the hill when the rain just quit and the wind simply died, so I went back to the stand to hunt after taking the wet crap off. I shot a buck deer at the waterhole, 20 feet away, from the stand ladder where I was getting the gun tied to the tether before climbing.
I've just learned over the years that there is no best time to be in the woods hunting. If I am not there, I have zero opportunity to fill a tag.