Can't help much on sheep, goats or pigs as far as particular breeds. But for chickens, I'd look to breeds that are sufficiently cold hardy to handle the occasional dip into negatives. Most will probably be OK with that. But also consider how hot your summers get, and make sure the chickens can also tolerate the heat. NC can get toasty, and quite humid. Most chickens will actually tolerate the cold better than the heat.
Here in the northern Puget Sound area of Washington (which, granted, doesn't as cold in winter, or as hot in summer) we've had good success with various Wyandotte breeds, Austrolorpes, Barnevelders, Welsummers, and Marans. All have been good layers and have handled the weather just fine. Only problems have involved a recent coyote attack that killed 7 of the 26 hens.
I think Justin Rhodes is in your general neck of the woods, and he seems to like Austrolorpes as a dual purpose breed for that area.
I don't know if chickens eat ticks as we just don't have a problem with them here, but guinea fowl are supposed to be the #1 farm animal for people with tick problems. But they're also close to the #1 animal that people are glad when they're gone due to the noise they make. If I had a tick problem I'd seriously consider getting some guineas, but probably would only get them occasionally and only long enough to reduce the local tick population enough to not be a problem for a couple years, then I'd slaughter or sell them.
For sheep, one thing I've learned on here is that they will clear brush. Maybe not as preferentially as goats, but they will eat it when they run out of other things they prefer. So, if you would prefer sheep over goats (sheep usually are easier to fence in, and less troublesome in general) that is something to consider. With both goats and sheep though you need to do something to protect any trees you don't want them to damage.