"Hunting" in the UK usually referes to chasing about with horses and dogs, "shooting" to pheasants, grouse etc. and if you tramp about mountainsides after deer it is "stalking".
Interestingly enough, in Scotland although most wild areas are privately owned everyone has a right of access - you can wander about pretty much anywhere that isn't explicitly private or where you would cause harm.
Here's a symptom of the cultural prevalence of hunting in the U.S.:
http://www.portal.state.pa.us/portal/server.pt/community/sta...
Most states will have such a listing.
There is also plenty of private land kept for hunting, which as you might mean to imply, is not cheap.