I believe the horses in the parks all have 'owners', but I'm quite sure there are some going spare up at the biodome. If you want to bring one down to the park, once I've got the millhouse properly organised I'm happy to house them in my stables for you.
If you can't find a spare up there, then you're welcome to ride one of mine. Preferably not the Shetland, mind you, but I don't think you're a madman.
Hopefully there will be a door soon and we can get some more livestock.