We've raised hogs for several years, allowing them to forage and root as much as they please, and we have yet to end up with one that tastes "gamey". Our hogs are in large pens (pasture and woods). Pigs are, by nature, omnivorous -- they can (and should) eat meat, eggs, veggies, grass, dairy, etc. They are very efficient composters. The only thing we don't feed them is, well, pork (though I'm sure if they tasted bacon they'd understand). Our breeders get rations of feed, and all the hay they want. The feeders get free choice feed and hay in addition to foraging and treats. They get lots of day-old bread, yogurt, etc. We don't get dry, white meat but rather a rose colored well textured meat with lots of juicy flavor.
There's a couple of things that make your life a lot easier:
-Invest in a hot-wire, and maintain it well. If they decide they want out of a net-fence, they're unstoppable. They quickly learn to respect electric boundaries (as have I!). I run my wires at 6 and 12 inches off the ground. If it hits them in front of the eyes they'll turn away from it, behind the eyes they'll run through it.
-Raising them on too much high protein feed will get their weight up faster, but the meat will be less flavorful and less marbled, and their habitat will tend to smell worse due to the massive amounts of undigested protein, which also encourages more bugs. Kudzu, brambles, blackberry canes, briars, hardwood tree trimmings... they love 'em. They'll eat earthworms like spaghetti noodles, and love to eat snakes. Rooting is where they get their minerals and find little goodies like termite nests and tree roots. They're very good rooto-tillers, mulchers, composters, and excellent at clearing underbrush.
-They are tremendously curious and playful; often when they get destructive or try to escape, it's their exploring instinct. throw a large hard plastic ball or a 55 gallon plastic drum in there and they'll entertain themselves. A heavy piece of knotted manila rope will incite a tug of war and a chase.
-Lots of fresh water and give them a place to wallow. Mud helps them shed dead skin, keeps the lice off them, and protects them from sunburn. Ours enjoy a "piggy-bath" playing in the hose spray when we have to fill their wallows up during the dry season.
-We always move them into the stock trailer or a clean separate pen with fresh hay and water for their last few days. It allows them to "clean out" a bit, and makes my job easier, and they are chilled out an relaxed. No stress on the animal and a lot less stress on me.
-Treat them with respect and always keep an eye on them. As fun and friendly as they are, even a small pig can hurt you (even a piglet bite on the back of the leg is painful). Our 600lb boar is a teddy bear, but he's still a 600lb boar.
-When their day comes, have a plan to get them rounded up. Practice moving them around often so they (and you) get used to it. If you're taking them to a processor, make sure you've got it arranged (sounds stupid, but I've seen folks turned away because they didn't call ahead. Sometimes processors are booked out for weeks.) you'd hate to take them on a round trip and stress them and you out for no reason.
Enjoy raising and feeding them, and they'll return you the favor!
-Dan