I suspect that you are tensing all your muscles as you push up the hill. The leg and back ones will naturally release to a certain extent as you swing each leg forward, but poor old neck and shoulders stay hunched. Try stopping at the beginning of the hill and consciously breathing out and stretching up with your head letting your shoulders drop down...the old puppet on a string posture.Then go up the hill steadily, if you feel yourself start to hunch then stop and relax again.
hth