I just moved into a new propperty that already had paddocks. It's on a mountain and the paddocks are full of rocks. Rocks the size of golf balls and baseballs. All sorts of them. Some rocks you just see a portion of them and others are lying in the surface.

Picking all these rocks out sounds like an endless job. Does anyone have any ideas on what I can do and if I have to add anything to the paddocks like sand?

well you'll have to just pick them by hand unless some of them are too big for that, then you can get a rock picker. get a bunch of kids out there and have them start making a couple rock piles outside the paddocks and you could sell them. lol

Are you concerned for the horses hooves, or more concerned that the rocks are taking up grass-growing space?
We have a good bit of rocks here in mid-TN, not so much that it's covering alot of grass space (we have alooot of pasture space) but for the amount of rocks and gravel we do have, helps maintain the hooves a little easier than if they were on strickly grass footing. I'd be trimming hooves alot more often, and would have a little more tender footed horses also if not for some of the gravel in the paddocks and pastures.

You could try using a rock rake to get rid of the loose ones.