I'd say that the condition of the animal is most important to flavour and tenderness.i.e. skinny animal can be rank and tough.
Time of year and age doesn't matter much.
Also be sure to age your venison before cooking (If you have the opportunity.) Hang it for a week in a cool place.
I have two nice stags hanging in my woodshed right now, they were shot last Tuesday (10 days ago.) It's been cold and I tried some steaks yesterday..mmmmm....
They were shot in full rut. (Rut is just ending here in NZ.)