Andrea - good questions! I can't answer some of your specific questions but I'll toss out something that might feel like knowledge.
First, go small. As the aforementioned KuneKune, or an AGH variety. Small is nice because they are easier/less scary to manage, require less demanding enclosures, and they won't tear up fields as much. Second, get a pig with a short snout as a long snout is associated with rooting and you don't want them digging giant wallows that you have to move fencing and structures around.
Breeding ... I've considered this but so far have declined and intend to stick with seasonal weaners. My opinion is that breeding hogs is a lot more like zoo-keeping than farming. Even AGH boars get big, other varieties get huge. The Berkshire boar at one of my providers rips 2x6 boards off the enclosure just to have something interesting to do and has to stay in an enclosure b/c they do to much damage to their pasture otherwise (this is one farmer's experience anyway - others may do better). So there is a lot of pen cleaning, carrying food, etc. In comparison my cows and bull are super simple.
Feed & Grazing - Breed is going to be really important here. The other thing is your expectation - standard meat breeds, even heritage ones, grow big fast, reaching a 250lb(ish) slaughter weight in ~6 months. They consume a tremendous amount to achieve that growth, far more than most pastures can provide without substantial additional feed. Smaller breeds put on weight more slowly, have lower caloric requirements and generally aren't economical for selling meat from (there are exceptions ... these are generalities here). So if you're ok with grabbing a six month old pig at 30-40 lbs and just popping it in the oven as a roast pig, you're fine. If you're expecting to sell some fancy chestnut fed pork, you might be disappointed. So if you're doing this for your own table, I think grazing is more viable.
Also, there's probably not much for forage in the winter and I'd expect to feed them.
As for wintering ... check out Walter Jeffries and Sugar Mountain Farm (https://sugarmtnfarm.com
). His pigs over winter in open pastures - in Vermont!
I'll hope others have actual knowledge and experience on your questions of hoof health.