You can get a fair measure of your horses immune system from the differential part of a regular blood screen, the SMAC 26 with CBC and Differential. The total immune cells in your horses blood are only a sprinkle, but 50%-65% of them are phagocytes called segmented neutrophils. Elevated "segs" usually means a bacterial infection, because as soon as an infection starts, your bone marrow releases neutrophils in massive numbers to combat it.
The second most common type of immune cells are the lymphocytes (25%-40% of the total white cell count). These are elaborated in the spleen and lymph nodes. They build immunity primarily against viruses, but also some bacteria and other foreign cells, by producing antibodies. Elevation of "lymphs" usually signal viral infection.
Then come the monocytes (4%-10% of total white cell count). They are transformed into macrophages that engulf and digest foreign cells and the dead and dying body cells that are causing the inflammatory reactions. They also suck up stagnant fluids that collect at sites of inflammation, so are crucial to reduce swelling and inflammation in sports injuries.
Eosinophils comprise 1%-4% of the total white cell count. They are specialized to protect the lungs and gastrointestinal tract, so are vital to performance horses. They also protect the skin and fight allergic reactions. Eosinophils are elevated in infections and illnesses of lungs and gut. High levels are also seen in parasitic conditions.
You may see other immune cells, such as basophils and bands, on your blood test. They are rarely relevant is sports medicine. The items we have covered are all you need to understand and use the research necessary to build a strong immune system.