You had to make a rational decision to have your horse put down, you did what was best for her and put your own needs and feelings aside. You had to put your defences really high to make a strong decision and it will take a little time for them to come back down again and for the reality to hit. So far, the way you've dealt with it sounds normal. In time, the memories of the happy times you had together will be comforting, but to reach that stage you have to go through the other stages that Zinco described in his post.