Yup. Equine blood and plasma are sometimes transfused. Horses have 7 different blood types - more types than humans - and each type also has factors, and blood typing is often used in breeding. There are more than 400,000 different blood type and factor combinations in horses, which means blood can never really be completely matched, so blood transfusions in horses are risky. However, horses are also more tolerant of mis-matches, and a horse that has never received a blood transfusion generally does not react to even the most incompatible blood. This means that in an emergency it's often safe to give a horse whatever blood you have on hand - it's not as good as better matched blood, but it can save the horse's life. And there are equine universal donors too.
There are, however, no blood banks for horses. Horse blood can only be stored for about a month, and of course, a horse needs rather a lot of blood. So, donor blood is stored on the hoof - either in specific blood donor herds (generally permanently lame animals donated by their owners for the purpose) or through a blood donor registry much like with humans. The vet might also test other horses owned by the owner of the sick or injured horse.