Or rather, everyone cool rides dinosaurs. This was one of the best things about Eberron, the dinosaur riding, but they did not, in my opinion, take it far enough.
No. In my setting, the halflings aren't the only ones with access to the dinosaur awesome. Everyone cool rides dinosaurs. The players ride dinosaurs, important NPCs like kings and bartenders ride dinosaurs, major villains in spiky black armor ride dinosaurs. Even plenty of people who are not cool ride dinosaurs. Like bards.
No one rides horses. (Even bards.) They might ride things that are significantly stupider than dinosaurs, but they don't ride horses.
A lot of the different knightly orders have running arguments about which dinosaurs are best. This has evolved into bi-yearly contests in the civilized realms, jousting and that sort of thing, where you're on teams depending on what sort of dinosaur you ride. When two riders of different sorts of dinosaurs meet, they have a tendency to engage in an impromptu dinosaur-measuring contest.
Non-dinosaur riders tend to think this is sort of stupid, but they tend to think that everything relating to dinosaurs is sort of stupid. That's the problem with dinosaurs: they're sort of stupid. You can train them, and some of them are less stupid than others, but there are some definite limits to their intellectual capacity.