In my area the game wardens give interviews on the local news shows and for the newspaper, asking hunters to please shoot does. And they have a big writeup every year in the fish and game law handbook. I try to follow their advice, killing at least one to two does for every buck I bring home. My lifetime ratio is about 60-70% does.
If there are spotted fawns with a doe in December it means that there are serious imbalances in the herd sex ratio so that does are getting bred very, very late in the season. It also probably means that there is a serious overpopulation problem. This leaves the hunter in a quandary, how do they reduce the deer herd without killing the does? Chances are that winter kill and coyotes will remove the problem away from human sight but I've got to admit that if the herd was so unbalanced that I saw spotted fawns in December I'd probably call in a report to the game warden and ask for advice.
If there are brown fawns they may be does or they may be bucks which haven't reached the point where the doe drove them away. These little bucks are a problem. If one shoots a "little doe", especially in poor light they have a 50-50 chance of it being an antlerless buck. This means that the only way to be sure to maintain sexual balance is to harvest mature does. By mid December if you see lactating does there is a population problem even if the fawns are brown.
What about does who have a single brown fawn? This is a bad sign but not as bad as late season spots. It means that either does are subfertile - a product of poor nutrition and overcrowding - or one of the fawns has died. Seeing one or two does with only one fawn isn't a pattern but if you see a lot of them it may mean overpopulation or herd imbalance.
When I shoot does I tend to shoot the ones with yearlings and not those with this year's brown fawns but I will shoot a yearling if I can definitely see it has no buttons. So far I've never taken home a button buck but then I pass up a lot of shots. I tend to pass up shots if I see a very young brown fawn hanging with the doe, but in my part of the world you usually see antlerless deer in groups of 5 to 10 so it is easier to choose your shots. I've been passing up shots myself this year because I'm seeing mostly single immature bucks and small groups of does, not the big groups of previous years.
So I've gone around the world here and not said much. Maybe you should call your local game warden for advice? They could tell you how healthy is your local herd.