Welcome to the HF, Mamber!
There is a lot, which comes into owing a horse. Even a min, or donkey, or a goat. Before getting them in (sounds like you just want pasture pets?) try to count all money you'll need. I can't really tell the amounts for minis, but here's been my experience with my big girls:
1) Feed. Hay is #1. I feed hay year around, because I don't have pastures. If you do most probably you can save on hay April - Oct. I have a feeling minis are not grained, but I may be wrong, so you may consider pellets, especially if they are starved
2) Shots, at least A MUST ones (like Tetanus, Rabbies, etc, you can google them up)
3) Trim (most probably you won't need shoes as long as they have healthy hoofs). Every 2 months (I go shorter in summer as they grow LOTS of hoof)
4) Teeth floating
5) Some health emergency fund if something would happen
6) Misc things like halters, leads, brushes, buckets etc.
7) Where you going to keep them. Boarding is more expensive, on own property - lots of work (you'll need good fence, area clear of dangerous obstacles, shed, water 24/7, salt block)
I'm sure I forgot something else
but that'll give you an idea.