It's too varies to give a definite answer. Many people who hunt may not shoot for recreation, many who shoot for recreation may not hunt that often. Then you have folks who hunt only one type of game, and those folks who hunt various types of game, and those who do everything (hunt and shoot) year around. It's really hard to say what's average.
As many rounds as you think you need to stay proficient and enjoy shooting is what I recommend. For you to decide, it's your call.
Personally I lose count. I shoot for many reasons, but mainly for enjoyment and to stay proficient. I reload for my biggame rifle and I hunt. I shoot many rounds of trap and sporting clays with shotgun per year. I also use my shotguns for upland bird hunts and waterfowl hunts too. I plink with my .22LR, but also sometmes hunt small game with it too. I stay sharp with my many handguns, for defensive purposes, not hunting. All different types of ammo and guns for different reasons, too many to keep track of. I do maintain accurate round counts for all my pistols and for my big game rifles, but not for my .22LR rifles, nor any of my shotguns.
There is one tip I have learned over the years in hunting whitetails in late season snow. Do not overlook soybeans left standing on the edges of fence rows, woods, creeks, buildings wherever it might be, this is where the deer will be while the food lasts during late season. December/January will pull deer in from some distance away to feed on the easy to get to food.
I killed one of my nicest bucks off of a very small patch of soybeans that was left after rains created a...