Are they wild? No, but they live as if they were wild. That Herd horses are free range horses. They are privately owned and lightly managed. The horses mainly exist with no assistance quite well. When there is a need, the rancher steps in to administer care or support.
Can you pet them? No, but they are often approachable. For the most part, consider them wildlife with all the considerations that goes with encountering a wild animal.
Do I cue them, use rewards or treats, or try to alter their behavior in any way to get the shot? No, but there have been occasions when I intervened when a newborn foal was in danger.
Do they roam freely? Yes! Their territories are fenced, but most of the spaces they live in are hundreds, or thousands of acres bordered by private ranches or federal lands.
Do the mares live with a stallion? Sometimes, but the stallion is not part of the herd year-round.
Do they spread wonder and joy to anyone who is fortunate enough to observe them? Yes, always.