I was going to ask my husband what he's suggest, but he's already fallen asleep. We have cattle too, so everything around here has to be cattle tough, so he puts many things on railroad ties, that's probably overkill for just a mini or two.
For the sides of the pen, you can probably get by with pencil posts; but will need bigger posts for the corners (6-8" posts) and to hang gates on.
Here's a picture of my now overkill mini pen; hubby built it for my senior half-Arab gelding, he passed on, so now its a mini pen.
Picture is just a corner of the pen, as I was taking a picture of my new barn.
Here is a picture showing the corral, but its winter, so mostly showing deep snow.
4x4 pressure treated posts are fine as long as you angle the top so the water runs off and does not settle on the tops (otherwise they rot). I use 6x6 posts for gates so the posts do not loosen in the ground from repeated stress and frost heave.