Its not that uncommon as far as i see it, to pee a horse has to be rather imobile compared to when they go poop, so when being ridden its not the best time for it. Some horses do it some dont.
My horse Banjo never did it while being ridden when i first got him. ever. But my TB Foxy , who i got a few years after boo , went pee on most of the rides, and pretty much once banjo saw him do it he started doing it too, lol. Now every now and then Banjo will go....not often ..but sometimes.
Is he a less dominant horse? if so maby its to do with that? he doesnt wanna be peeing on what could be some one elses teritory????
Im not sure, but honeslty as long as he goes at some point and its healthy pee i wouldnt worry to much.