Horses commonly get cuts on their lower legs from barbed wire and other objects in the pasture. Many of these cuts are superficial and not serious. However, some of them can be deep and can affect important structures like tendons, ligaments, and joints. Horses have very little tissue on the lower leg between the skin and these important structures, so a cut does not have to be deep to cause a major problem. Any cut on the lower leg should be seen by your vet as soon as possible to determine the structures that are involved. I get many emergency calls from owners with horses that have been cut on the lower legs and blood is squirting out of the wound and the owners are really upset. If you haven't seen this before and don't know how to handle it, it can be scary.
However, the most important thing to do is not panic because this increases your horse's anxiety. The most critical tools to have in your trailer or barn are non-stick pads, roll gauze, roll cotton, and vetwrap. I have never seen a lower leg cut for which a good wrap would not stop or at least slow down the bleeding enough to prevent significant blood loss. The key is to apply a non-stick pad to the wound and wrap that in place with roll gauze, then apply a 1-inch thick layer of cotton and wrap as tightly as possible. If you apply enough cotton around the leg, you cannot wrap the leg too tight because the wrap will only be on for a few hours. Also, it is important to not use any medication as some medications will prevent suturing of the wound, so the most important thing is to wrap the wound tight and wait for your vet.