In the snow, his feet don't have ice balls in them , to they?
I think that when a horse has behavior problems going to one side only, there is almost always some sort of comfort issue. Something in his body is hurting when he goes to the right. Does this happen only when CANTERING to the right , or while trotting to the right also?
When this happens, do you pull harder on the rein or put your leg on and ask him to go more forward? The rearing thing makes me think that he gets stuck. Somthing hurts, he starts to buck or try to run out from the pain, then pressure on the bit means he has nowhere to go so he goes UP.
If the behaviour continued every time , and was at all gaits going right, I would have him looked at by a vet and/or a chiropractor.
As for getting off him and lunging him, I don't see the point there.
You want to end on a good note with him. Good means that he is doing what you ask and doing it reasonabley willingly. If I had no luck getting him to go right, I would ease off, then go left and set my goal to having him responsive to the left before calling it a day and gettting off.
The feeling that you have between you at the moment you get off is the thing that sticks iwth the horse afterward. So, find a goal that is reachable, get it and get off.