It all depends on the area I think and my base for that is the creature you encounter in said area.
The underdark for example is mainly very large tunnel with the oddities of the squeezer part, I mean.. you meet carrion crawler and the bulettes in there so even the tallest horse would fit without the slighest problem, escpecially in mine complex where carts rolls by, if big carts are being rolled on, then surely a pony can fit without a problem.
Underground cities complex is another place I could imagine mounts fitting.
However there is some underground complex I can't imagine a four legs in there, but that goes true to centaurs and the likes too of course.
After that thought, the main problem is how you access to the underground place, is it a cave carved in the mountain side?
Is it a place you go with a ladder?
Is it via staircasse ? spiral or not?
I mean horse can easily go down a straight staircase, old medieval european cities have still marks of stairacases in the street made for horses. And even modern police horse in Europe are trained for that (and for not moving an inch when firing guns are involved).
As for mounts not loving to be inside..I don't really know where that ideas comes from, for mounts are been used underground since mining was invented many millenia ago. For some modern idea I would link to
http://kycoal.homestead.com/MiningtheCoal.html as example of hand-made modern mines where mules and pack horses are used, and that's mine made by modern humans, without the mining backgroup of fantasy dwarves, the magic means of drows and the godly power of those who made the underdark.
Now... there is always an IC way to get a pony to go down there, I think it is the Harpell who reduce horses to the size of a plush to stable them more efficiently.
But that is integrant part of a roleplay and should be acteed accordingly.
I think that lke a lot of things in RP, it is a case by case basis depending on how it is rped out that gives credit or discredit to a situation.
Brar
PS: Just one last thing, just to remember. Mules are crossbreed between horse and donkeys, and are horse sized (Large in DnD) which means far larger than a pony (Medium in DnD).
So In size it is Horse/Centaur/Mule > Pony/Donkey/Wolf