Legal rural hunting for millions would be vanished, and the chances would be drastic enough that an illegal gun black market would form, basically leading to another Prohibition.
I mean I know it's apples and oranges, but even in the UK rural hunting is still very much alive and well; anyone can get an air rifle, and go hunting for small game (rabbits, pigeons etc), and it's relatively easy to get a shotgun license.
You can go deer hunting in Scotland (although we have the problem of not enough deers) and I've shot a .22 in Scotland with someone who has a firearm license.
The restrictions come from who can actually buy/own the guns; rather than hunting.