I tend to approach war mounts and steeds from a regional perspective, rather than species.
For example, in my interpretation of Mystara:
-  If you are from Karameikos, Ethengar, or the Heldann Freeholds, you’re gonna be riding a horse or worg into battle.  Or a nightmare if you make a trek to the World Mountain in Ethengar.
-  If you are from Glantri, it’ll either be some type of construct, elemental, monstrosity, or undead.  Preferably one you made or summoned yourself.
- If you are in or from Alfheim, you’ll be clinging for dear life to the back of a dire gibbon, especially if it swings through the tree branches.
- If you are from Rockhome, it’s gonna be either a rockhome lizard if you lived underground, or a mountain goat if you lived aboveground.
- If you are from the Northern Reaches, you’ll be riding an axe beak.  Or a woolly mammoth if you’re a member of the nobility.
- If you are from the Broken Lands, it’s gonna be a giant cockroach.  Or a construct if you buy one from the gnomes.
- If you are from Thyatis, congratulations.  You get to ride a triceratops!  Or a griffin, if you’re a member of the nobility.