Many of the expenses will be region specific. A mini still needs it's hooves trimmed every 6-8 weeks, and that can range from $15-50 per trim, depending on the region; don't expect it to be cheaper just because it's a mini (and there could be a trip charge on top of the trim fee, especially if you have the only equine at the stop). Deworming will cost you a couple tubes of dewormer a year tops: so maybe $20-25 at most. At least some hay will need to be purchased, how much depends on if you need to feed it daily year round, or just during the winter and they can graze during the summer; hay prices vary by region, I've seen it priced from about $5/bale to over $20/bale (and about $125/ton to like $400-500/ton). How much hay you'll need will depend on how big the mini is and how many months of the year you need to feed hay; a smaller mini around 250# is going to need about 1 ton for a whole year, a larger mini in the 350# range will need 1.5 ton for the year or a bit more. While many minis don't need much for grain or supplements, they do need at least a ration balancer or vitamin mineral supplement to make up for what all forages lack; for one maybe $20/month for just that, more if they are a harder keeper so need more feed. Plus you'd have your initial expenses of the buying, transporting, picking up necessities (buckets, halter, lead, grooming supplies).
I've not broken down what I spend per head, so not sure what it costs me each; but I know I spend plenty to keep my baker's dozen, or a little more, minis plus two saddle horses and a mini donkey fed and healthy.
That's all I can think of this early in the morning.