Selling your horses is a great way to make more room on your farm and to make money. The price that your horse will sell for depends on many factors (Age, amount of training, color, breed, COI, genetic potential, competition records, etc.). One thing to remember is that once you sell your horse, the horse is no longer yours and whoever bought the horse has the right to do whatever they wish with the horse. If you don't want someone to do whatever they wish with the horse then simply don't sell the horse.
Studding your stallions out is another great way to make money and to expand your horses' lines. The right stud price of your horse depends on many factors (Age, amount of training, color, breed, COI, genetic potential, competition records, etc.). The "Approved Mares Only" feature isn't functional as of right now and therefore any stud you put up is technically a public stud where anyone can breed to the horse. Though it is very respectful and considerate to not use studs that are private studs only. It is best to ask the private stud's owner for permission to use instead of using at your wish. To prevent private studs from being used, try transferring horses, have the horse up for only as long as you need, and/or putting the horse up for a really high stud price.