DISCLAIMER: I can only speak from my perspective and understanding, and I'm less experienced than most of you. I apologize in advance... I nonetheless will do my best to give helpful feedback.
LibraryAdventurer's Condor: In testing, I felt the gain option added little to it. I recognize it's remnant of the thematic Smuggler effect you planned, but I would consider removing it (so I guess this would be Eagle or something). Also I don't count it against you but I wish there was a slimmer way to express those favor-based dismount conditions. I couldn't think of one. In any case, it was a fun and very useful card! It worked well as a mount, and worked well within the deck. For allies with low favor cost, it can be basically a permanent mount. With high favor cost, you can re-mount it as you need to, while the dismounted ones cycle through and give extra favors.
emtzalex's Unicorn: Obviously since it's worth a Duchy if unmounted, you would likely only buy it with the intention of /keeping/ it mounted. Basically I'm not judging it as a 7-cost Duchy, because you'd only do that under certain circumstances -- this will commonly be bought as a 7-cost %5 that causes you to discard each turn. Naturally you would just want to mount it near the end so you don't have to deal with the discarding. The more you've greened (and the less turns left in the game), the less of a sacrifice it is to keep Unicorn mounted. Victory pairs well with Mount, since it keeps it semi-Exiled. This is well done.
Xen3k's Hippocampus: Well-priced based on playtesting. I'm not an expert on card phrasing, but in the Mount effect, is there a way to clarify that you can return the card to the bottom? I saw that in your description but that wasn't my impression when I initially read the card. Anyways: to make the most of your $, this is certainly best bought as a mount, but as a cantrip is inoffensive in most decks. I like the interaction between the mounted and unmounted Hippocampi. Very fun card!
J410's Crane: You'll want this to be Action - Duration - Mount, but no big deal. Crane plays pretty differently depending on Buy availability in a kingdom. The Bridge Troll-top part is attractive, you just have good Buys and $ before you can fully take advantage of it. Very nice synergy with mounted and unmounted Cranes.
segura's Donkey: The top compares most directly to Warehouse, but with larger hands and more variety, can potentially sift with greater reach (but worse reach if low on hand size/variety). Bottom is Hireling that lasts until you buy Victory, well-priced and attractive at $5. Even though the Warehousing can be underwhelming in kingdoms with less variety, it's non-terminal so it doesn't usually hurt when it dismounts (aside from losing your Hireling effect). Very cool!
Aquila's Alpha Wolf: I'd change "lose" to "remove", like Butcher, but maybe that's personal preference. In any case I love the top part! The mount effect is cool, especially in kingdoms without Villagers (most kingdoms) -- I like that it gives multiplayer interaction without attacking. If other players are paying attention and have the option, they can skip over Actions you've played since your shuffle to keep your Alpha Wolf pinned. However this card also has an unspoken rule that you can look through your discard pile at any time outside of your turn. Not necessarily a bad thing or a big deal, but interesting to note.
Can I first just say: WOW! Amazing cards all around! You each brought something unique and great to the table. There was not a single submission that I didn't enjoy playing with. Give yourself a pat on the back! After great agony, here is the decision I made:
HONORABLE MENTION: J410's Crane
RUNNER-UP: Aquila's Alpha Wolf
WINNER: Xen3k's Hippocampus