Here's a card I came up with a while ago:
He essentially serves the purpose of getting Gandalf where he needs to be quicker by bringing him into play quicker (making him cheaper) and bringing his aid to help defend against an attack (by adding his defense to a defender).
The other real thematic possibilities for mounts involve either readying or location control, but there's enough of that. I wanted to do something new. Something that would be especially good for Gandalf. Adding 4 defense to a character is a huge boost, but it comes at the cost of exhausting Gandalf. This isn't a huge deal since you are likely using the Hobbit Gandalf if you're using this card, so you can still quest (since he doesn't exhaust to quest), and if you end up not needing Gandalf to help with defending, he is then available to lend his 4 attack to help destroy enemies.
This card essentially just makes Gandalf more versatile by giving the option to allow Gandalf to help with defending, rather than by defending alone. This can make Gandalf a very powerful card in Hobbit decks where you have Frodo as the defender, but you want to keep your threat within secrecy range, so you give Frodo more defense so he receives less damage.
Also note that the defense boost lasts until the end of the phase, so if the defender has readying effects, he has the boost for multiple attacks.
In case the image fails to load, here's the card as text:
Attach to Gandalf or put into play unattached.
Forced: After Shadowfax is put into play unattached, play Gandalf from your hand for 2 fewer resources than his printed cost or discard Shadowfax.
Response: After a character is declared as a defender, exhaust Shadowfax and attached Gandalf to add Gandalf’s defense to that character until the end of the phase.