Howdy, you simply just ask to breed with the horse by clicking “breed.” At that time, it is up to the person with the stud to accept or decline it. I believe it doesn't cost any money unless it is accepted obviously. Sometimes though, players put up horses for stud for friends or other players. If you are interested, I would just ask :)

thank you! :)

You can always check out the horses owners account page, a lot of us will include info about private stud / broods as to whether or not you will be insta denied or any requirements your horses must meet to be accepted.    A LOT of 1 bit privates are aimed at ‘breeding partners’ or alt account use for campaigns or projects, or agreed upon 1 / 2 time breedings.     As Westernwind said though, if you cant find that info on a players page, and want to double check prior you can always ask.    Usually private studs / broods up for more bits or ingots are for the most part free game.   Worst case you get denied :)     I would just make sure to be mindful of the 1 bit private ones though