I need to get livestock up to my house! (Minecraft)?

I built a house way up at the sky limit & need something more than chickens because a egg factory is too big for my new house, I tried lead but it killed my horse via fall dmg when I got up there.

Make a water elevator and then lead the animal over to it.

I would say make a walkway of about 3 wide up to your skyhouseand then you can use a lead… I'm sure it's a lot of blocks, but a cow going up a water elevator is going to go up, but I don't think it will walk on your land by itself lol