In Skyrim, is there a way to heal my horse while I'm on it? What about a dragon? I know that if you have the healing hands magic, you can heal a horse while you are not on it, but is there a way to heal them while you are on it (since you can't use magic or staves while on horses)? I have noticed that even though you can use magic while on a dragon, you cannot use healing magic (including magic to heal yourself). Is there a way to heal your dragon?
From what I've seen, it looks like you're only able to heal your horse while you are standing next to it, rather than riding it.
As for healing your dragon, based on the Healing Hands wikia page, it looks like it will work for your dragon mount, since dragons are not listed as exceptions.
It will not heal undead, atronachs, or Dwemer animunculi.
However, you can't cast it while riding, as it's not listed on the list of spells/shouts you can cast/shout from dragonback here.
As stated in both the question and the other answer, you can't heal a horse while riding it because you can't use spells while riding a horse.
As far as riding dragons is concerned, it is possible to heal both it and yourself while riding one by casting Grand Healing. I've done this myself. I play Skyrim using the Legendary Edition patch 1.9 on PC with no mods installed. That includes not using the unofficial patch.