Since most all my hunting any more is stand hunting, I prefer cold frosty mornings with light winds. I will not hunt when the weather is really warm or hot, I simply do not enjoy it as much. We are lucky here in Tn & Ky that the seasons run during the primary & secondary rut. Most of the influences I use, reference deer movements, are tied to the rut and bucks looking and/or chasing.
I also prefer to hunt mornings over afternoons, not enjoying guting and dragging in the dark as much as I used to.
I'd have to say my harvests are split between morning and afternoons, but I most enjoy getting to my stand an hour before SR and watching the birth of a new day as the woods wake up. I will hunt most any weather, especially at the beginning of a season. Heck I was out yesterday morning in sleet, snow & rain for several hours.
The biggest buck (rack-wise) I ever killed was on a nasty rainy morning. The biggest buck I ever killed (body-wise) was on a cool, clear morning after a night of hard rain.