nirons - horses are generally hobbled at night. There is no horse feed available outside the Ulaanbaatar. It is sold in huge flour sacks and if you choose to take it, you will need a big feeding bowl to mix it with water, and an extra pack horse. Contact Stepperiders - they teach all this stuff. Including how to avoid horse thieves - a very real problem for solo riders in Mongolia. Stepperiders might also be able to put you in contact with others who are planning the same type of trip.
Going by yourself randomly into the countryside to buy horses is a crazy idea. First of all you will be very lucky to find anyone who speaks English, and the horse owners definitely will not speak English. And horses are the easy part. You also need to plan your gear, your food, learn some customs, buy equipment (like hobbles and saddles), and plan a route.