Bambi is supposed to be a whitetail deer in the film adaptation. White tail deer give birth in the spring and the young fawns lose their spots and become independent by autumn when the mating season begins again. November is when hunting season tends to take place. Bambi’s mother is shot by a hunter in the winter, and Bambi is still a very tiny fawn with spots despite being born that spring.
With or without his mother, if Bambi was that little and under developed by winter he would die of exposure to the elements because he was tiny and stunted, having not grown at all in the half a year he had to mature. There are no little helpless spotted fawns around come winter.
That, and Bambi’s dad would have been more likely to kick him to death in a fight over food than actually look after him.