It’s been years since I’ve done this, but this is what I remember: I’m pretty sure you need to export the fbx with all of the animations in it. Import it into UDK. In the editor, make an AnimTree that blends together all of your animations. For any animation node or skeletal control you want to access in script, give it a unique name. Then in your vehicles class’ PostInitAnimTree event you’ll set any variables you’ll need to access those animation nodes or skeletal controls.
Are you familiar with UDK AnimTrees and skeletal controls? There was a tutorial somewhere that showed how to animate a guy doing bench press, using UnrealScript instead of a built-in animation. That might be a good place to get started if you can find that.
You’ll probably want a movement animation with the horses walking and the wheels spinning. For faster movement, you’ll have the horses running and the wheels spinning faster. To blend between them, multiply the animation speed by the vehicle’s speed, and then do a blend by speed to switch from walking to running. You may want to practice on just the horse at first until you get the hang of it. Also be sure the footsteps line up between the walking and running animations, or else the blend will get messed up. (There was a detailed GDC talk about that. The game the girl worked on was the Flame in the Flood, I think.)
Backwards movement should be easier because I assume you won’t need a backwards running animation.
You’ll also want to set up animation nodes for turning and turning in place. Those will make use of the front wheels turning left or right.
I don’t know what animations you’ll want to call in code. I think the AnimTree should handle most of what you’ll need. Probably opening and closing the doors would be handled in UnrealScript.