Ringoblack
Both private clubs where I've been a member in the past always closed the course after the first snowfall in November, or whenever that occurred. They treat the greens for snow mold, then put down a thick top-dressing of sand as an insulation barrier.
When we'd come back out to play in late-March or April when the course opened, the greens were as good as they would be at any other point in the season. For sure, keeping traffic off of them during the winter months helps. It's impossible to repair ball marks when the subsurface is frozen, so they get abused quite badly obviously if they're open for play during winter.
The only kicker is that the local munis (around here) can't afford to shut down when the weather permits, even if it is winter. They need every ounce of revenue they can muster.