Will this house work for my goats?

I'm currently 20 years in interior Alaska but having spent several years at Ft Bragg, I realize the old adage is true "If you don't like the weather, give it 5 minutes and it will change" really applies to NC. Your choice of shelters is totally up to you as to how much you want to spend and how fancy you want to get. I wintered 2 goats (a Togg and a Nigerian) thru 3 winters with a Walmart tarp garage and a couple extra tarps for sides and it was -40 and colder a lot of time. As long as they can get out of the rain / wind / snow, have plenty of good hay and clean unfrozen water they will thrive. I had their manger under the cover too so the hay way dry and the wasted hay /poop / urine composted it and generated heat for them too (deep bedding method). As for you in NC, you probably need to focus more on hot sun protection than cold weather protection.

PS. If you go with wood floor, consider covering the floor and part way up the sides with a scrap piece of linoleum. Then you can hose it out