4 weeks--ouch! Just think when you get back on the summer heat will be full on. Oh well.
When you start back please realize that your healed arm will be MUCH weaker than your healthy arm. You will have to concentrate on keeping your contact equally strong in both hands. I am sure you will be given exercises for your arm--be sure to do them! It will take a while, be patient with yourself, otherwise you will badly affect your horse (uneven contact etc.).
Take care. I know it is frustrating.