I don't really have any problem with letting my horses graze when it is clearly my idea. Anytime we're stopped for more than 5 minutes or so, I jump down and loosen the girth and if its been a longer ride, I also let my horse graze for a bit. If you have a "snatcher" on the other hand, I don't put up with it at all.. These are the horses that I never let graze while tacked up.
My mare understands when she is allowed to and when she is not to, so I let her when we're not on the move. My gelding doesn't. He'll snatch grass any chance he gets and if you're not paying attention, he'll get his face down there and just eat. He rarely gives me this problem, but he can be a turd for my boyfriend, who cannot quite anticipate him just yet. So, anytime I ride him, I just don't let him graze. I don't want to encourage that behavior at all.
If its your idea for the horse to be grazing, I wouldn't consider it a problem unless it developed into "snatching" without permission.
As for drinking, let the horses have their fill, especially in hot weather. Just take it easy on the trail for a bit afterwards. Some horses get "fresh" again after drinking, so they want to go, go, go.. If your horse is like that, I can see restricting it to a degree, but for the most part, let them drink. I'd just tell him to bugger off.. ha