Well, in Bambi: The Reckoning, his grief goes on a whole completely different path, which we see in this horror trailer.
What gets less remembered is that the movie does end with Bambi as a fully-grown adult buck, presumably living a peaceful life with his mate, Faline. Cue record scratch: But what if Bambi didn't live ...
Nevertheless, Bambi does grow up to be a handsome buck who finds love and becomes the next Great Prince of the Forest. Everything ended with sweet joy and we could all sleep at night in peace.