I would expect maintenance and upkeep would be more expensive for a horse than a dog. For example, you can keep even the largest dog inside a house. Most cities will not let you keep even the smallest horse at your house. Do you live in a rural area? Can you pay for boarding?
To buy a miniature, depending on whether it is registered(wich most are), or the colouring, The price can range up to the high thousands. I got a miniature about a year and a half ago and she was selling for $900.00. She was not broke, not registered, and no special colouring. But i love her. Good luck, and if you want any more advice or want to no anything else about darling miniatures just let me know.