You might be a tad small to manage your own horse. I'll make you a deal. Why don't we start you off with a dog and a cat or two dogs or two cats or whatever you like.
I have a horse though in stables here. I'll gladly share him with you. And if you can show me you can take care of a horse, groom him, clean his stalls, properly exercise him, then I'll get you a horse of your very own.