Open when the weather is hot-close when cold.
Morning George! I'm sure you will receive more detailed answers from experienced contractors, though can tell you it isn't strictly a seasonal thing. We open our vents in late spring/early summer to get air flow through so humidity doesn't build up down there causing potential mold and also weighing down pinned up insulation.
*** Last year we had vents inistalled that automatically open/close based on temp. IF the cooler season has a few very warm days, they would be open and in the warmer season, should the days get cool, they close. (I'm not sure if a day or so is significant, so not really sure it is necessary, BUT I don;t have to worry about when to open or close them!) I did have a recent question about the crawl space door as I had been switching from a solid door in winter to a vented door, then realized that when we bought the house, the door was a permenant metal door that always stayed closed/locked!
The new trend is to seal the crawl space completely year round. But prior to doing so you need to be able to control moisture within the space. Many of the crawl spaces I have seen in NC were soil floors on uneven surfaces. Making this project difficult. But doable. If there are heating ducts, or plumbing pipes in the exposed crawl then ideally you would want to bring them into the building shell environment. But as JP S stated open in summer closed in winter if you want to leave things as they are.
Be sure to look around in the crawl space for mold. This fuzzy growth will develop in a cool damp area quite quickly. So if mold is found, get it cleaned properly and then seal the area from moisture so it does not occur again.
George, Your vents should never ben open. Sealing the crawl space is what you need to do. Check the department of energy's site at www.crawlspaces.org for more information. They actually did a study of crawlspaces in NC that your might find relevant. Sealing, putting down a heavy vapor barrier and if it's damp you may need to consider dehumidification.