Doe, with the only exception being that the fawn was unusually small. I would likely pass all together in that scenario. (That being said, that very small fawn has a slim chance regardless of surviving the winter). Once this time of year rolls around for (late Oct and later) the fawns are very likely to survive without the (parent) doe. Once the does start breeding, the fawns get separated from the parent doe anyways, and in many if not most cases, the fawn will simply group together with another doe. The same happens if a doe is taken during hunting season, (or road killed, or taken from predators) the fawn will group up with other does and fawns. That's why later in Dec or later into winter it it not uncommon to see a doe with 2 or 3+ fawns with her, they are not very likely all her fawns.
Every deer hunter has their own beliefs or standards for hunting deer. This is my opinion, so take it as that. I think taking a doe, is a much better option to taking a smaller buck anytime, especially in areas like where I hunt in Ontario, where buck to doe ratio is low. Leaving bucks to breed as many does as possible in the first rut (early Nov) is very important. A doe that doesn't get bred while in heat, which is a short window of time, will not go into heat again for another month. If she isn't bred again during her second heat cycle, now your looking at her not getting bred until January. Gestation period doesn't change because a doe is bred late, so this means fawns are born a month, or two late. This results in a fawn that has little or no chance of surviving the following winter. Buck only hunters only worsen this buck

oe ratio, resulting in more and more 2nd and 3rd rut breeding, and more late small fawns the following year. I understand the guys hunting for a big buck, looking for a trophy, but if you are a meat hunting, I would take a nice tasty doe over a buck, simply because its a buck any day.
JimmyJames8, There has been several studies to conclude what you said is correct. It is said that if a doe raises a buck fawn, that in the following spring that doe will return to her home range, and she will then run off the yearly buck, which studies show that that buck will go miles away, completely out of area. This is natures way of helping to prevent inbreeding. In the situation where the doe is taking during hunting season, the buck fawn will return to its "home range" the following year, but will not be run off, therefor he will stay there and be another buck in your area. This helps keeping bucks in your area, and helps with the low buck

oe ratios.