When a vet sees that an animal is anemic, we have a very specific set of steps we go through to decide why.
1. If the total protein in the blood is also low, it means it is from blood loss. This can be due to a wound (internal or external), a bleeding ulcer, a very high blood sucking parasite load, etc.
2. If the total protein is normal then we have to decide if it is due to the body destroying it's own cells too quickly or due to the body not producing them fast enough (red blood cells only survive for a period of time in the body before they are recycled and replaced by new cells being released from the bone marrow).
If the body is destroying them we have to decide if it is due to a tumor, an auto-immune reaction, etc.
If they are not being replaced fast enough we have to decide if it is because there is something wrong with the bone marrow or if it is simply due to an on-going illness which is the most common cause of anemia.
In your case it sounds like your vet is thinking that it is due to the pneumonia and once that is resolved the body should be healthy enough to catch up and all will be well.
Supplements for anemia in most cases pretty much a waste of money once you understand how a horse becomes anemic. You have to get at the underlying cause. Giving a supplement to a horse who has a balanced hay ration but has an infection or other disease causing the illness will not make the body produce blood cells any faster. One such example is Red Cell. It is mostly an iron supplement and the only horse I have EVER seen with an iron deficiency was a horse who was box stalled, never turned out and had a poor quality diet. It takes very extreme circumstances like this to create iron deficiency and so you can see that giving a horse who gets a good diet and has access to dirt extra iron is a waste as they just poop it out.
Hope that helps!