Also as your training progresses, your horse will learn to breath 
correctly--something you can't teach directly but can influence by 
controlling your own breathing.  Take a very deep breath, hold, then 
exhale as slowly as possible while you are trotting at a slow to moderate 
pace.  And don't be too concerned about "hard conditioning" right 
now--remember long, slow, steady does the job better!
When you dismount, stand by your horse and breath slowly, drop your 
shoulders and relax your posture, do a soft focus on the whole 
horse--don't just "stare" at the flank--and present a calm, relaxing 
image.  Your horse is anticipating "more" and his rapid breathing could 
simply reflect a "ready posture".
Give him time.  It took our Freddy 2+ years to get the breathing down pat.
Diane @ Safe Haven
Allentown, PA