Not cranes, necessarily, but the yardarms of a ship are good for hoisting in and out heavy things, like boats and cargo and horses/mules/whatever. (The yards are the long wooden pieces that run horizontally across the masts; you can see several in this image of "HMS Surprise".) Generally, horses and other squirming cargo would be hoisted with the help of a sling, like so.

(Edit: To be clear, the Surprise is a replica ship modeled after a 1757 frigate; the early European settlers had ships that looked more like this or this, but the principle is the same.)

Horses can swim. Could you not just push them over the side when you're near the coast, and let them get there them selves?

EDIT: I don't claim to be a horse expert, and I was asking a question, not making a statement. I don't get why I've been down voted so harshly?