In theory all the adults are supposed to make decisions. However, there may be a ruling council. What appears to me is that there is that Mr. Threehorn and Grandapa Longneck seem to hold the most sway and that the rest of the adults generally follow one or the other.
Considering that the Combined Herd likely was created from several separate herds with a leader for each, it's likely that they were loathe to have a leader of a kind differnet than them rule over them. Eventually, they may have given some way into having a subset of leaders, even if some aren't their kinds. As far as can be shown, they do not yet have a single leader.
As for how things were run pre-first movie, that's a good question. Presumably the Great Valley was settled by Leaf Eaters since Doc was far younger and was certainly settled all of Mr. Thicknose's life.