The thing is, there are any number of situations in which horses, vehicles, and other ridable mounts are perfectly acceptable and cool in Star Trek.
Where they SHOULD be:
1. The Holodeck
2. On the surface of alien worlds
a. Horses on pre-industrial worlds
b. Cars, etc. on pre-warp worlds
c. High-tech vehicles on post-warp worlds.
Where they SHOULD NOT be:
1. In your inventory
2. Seen being ridden through ESD or Qu'Onos
3. Anywhere on your ship but in the Holodeck
If we follow these guidelines, then there is no reason to *not* include them. They belong here, in the proper places. They are part of Star Trek.
I mean, good heavens! Can you not see an Exploration mission in which we are on the surface of a pre-warp world, under cover, riding around in the alien equivalent of a Model T? If you can't then you aren't stretching your imagination anywhere near far enough.
Why not on my ship? I can think of a hundred reasons to have a pony on my bridge. Should be like the pets we have now, except instead of it spawning beside you, it beams in with you and you hop on it. You can ride around ESD to the vendors faster.