If your horse is having nosebleeds after a strenuous exercise then it's probably actually coming from the lungs. (still something to be concerned about). But if your horse is having unexplained nosebleeds with no obvious cause then that's a big concern and could actually be something that is life threatening. The fact that your horse has quickly dropped weight in a short time is most likey tied to the nose bleed. That and the lethargy, I would put in an emergency appointment call. Your horse could very likely have a life threatening issue.
I hope he's ok.