Is the exercise hard, or just a gentle trot and slow canter, if the latter then get a vet tosee him.
If its only after hard work then take him back and buil up your exercise slowly.
This can happen in older horses. Remember keep him out as much as poss, this will help his COPD
You've probably had advice about the copd, but there's some to be found here
It seems nose bleeds can be quite common in horses, and are mainly nothing to be too worried about. Type 'horse nose bleed' into Google, and you'll find quite a lot of discussion about it.