This seems a bit gratuitous.
I get the love/hate relationship locals can have with seasonal visitors but isn't the point of this forum to ask Qs about OBX as a vacation destination? Or at least that is how it is described on the homepage.
I think Tim was being facetious in his response, but this question gets asked so often hear that there does seem to be some semblance of a misunderstanding. Part of the problem is that the "Outer Banks" is more than a 100 miles long with a travel time from Carova to Ocracoke of more than four hours under the best of circumstances. So much information about offseason activity gets muddled.
Regarding Duck to Nags Head, short of mini golf and parasailing, most everything remains open in the off-season, particularly if it caters to the 30,000 people who live full-time in the area. As such, most restaurants, fast food, grocery stores, shopping, etc. remains open.
South of Oregon Inlet (I cant speak to the northern areas), things start to get quiet In November. The grocery and general wares stores stay open year round, but depending on labor availability, weather, economy, etc. some seasonal businesses stay open a bit longer; others close. Keep in mind that fishing is still big business in the fall/early winter on Hatteras. By January, most seasonal businesses are in hibernation and will re-emerge in March or early April.
There are always a few restaurants that stay open through the winter, but not many, and even they may be open a few days a week. Last winter Tavern on 12 was a godsend, being the only place in lower Hatteras opened over the winter. Sidebar: It's funny, I eat out more when I'm down in the winter because its usually just me, I'm working, and I'm only in for a few days. Not circumstances that make me want to do cooking.
This year I expect a lot more places to stay open this year on Hatteras until New Years. But nevertheless, you really never know unless you check their Facebook pages or websites.