Chris,
We normally tag and vaccinate within the first four hours. Some vaccinations have to be done in the first few hours to be effective. As long as the doe has both fawns dried they are ready to tag. The only time we had trouble with a mother not accepting them after tagging was just before dark and a heavy rain. We tagged too soon, the afterbirth wasn't all out yet. The doe ran off and never did accept the one fawn. Like Jonathan said all fawns are different, but I wouldn't be concerned about lethargic fawns until at least a weak. Not sure where you are from, but in Ohio 50 degrees wouldn't be a concern. We've had fawns in sleet or with frost on the ground. Cold doesn't seem to bother them, wet conditions or mud have always been my problem.