In the old days, when curmudgeonly grandfathers ran home maintenance, they'd go close off all the crawlspace at the first indications of frost. The reasoning was simple - once winter set in, leaving the vents open would chill the occupants and freeze the pipes. Best to close them early.
Those old houses, built up through the 1960s often had no insulation in the floor of the home. Heat rises (it doesn't, really, but hot air does) so they did not see the need to waste the money on insulation in the joist cavities.
Fast forward from 1940 to the oil shocks of the mid-1970s and suddenly we were greeted with a renewed interest in energy conservation. We increased attic insulation levels, moved from four-inch exterior wall framing to six-inch and, surprise, found that insulating the crawlspace made a lot of sense.
Grandpa still closed the vents, though. Old habits die hard.
What no one explained to them was that the vents for the space are designed to relieve moisture from the sub-grade spaces. Once we moved the thermal barrier into the flooring system, there was no reason to close them as getting water vapor out far exceeded any energy savings.
The current code is to have at least one square foot of ventilation opening per 150 square feet of floor area with an opening located within three feet of corners. Obviously, home inspectors don't measure this. Still, we can eyeball it and, more importantly, can identify problems that arise from improper venting.
Reporting on the crawlspace ventilation is a mandatory part of a Washington State home inspection. WAC 308-408C-150 states, "Insulation and ventilation. The inspection of the insulation and ventilation includes the type and condition of the insulation and ventilation in viewable unfinished attics and subgrade areas as well as the installed mechanical ventilation systems. (1) The inspector will: Inspect the insulation, ventilation and installed mechanical systems in viewable and accessible attics and unfinished subfloor areas"
The purpose of ventilation, moisture removal, makes a big difference in the overall health of the crawlspace and the structural components located in there. High moisture levels lead to potential pest intrusion and mold growth. Subterranean termites and anobiid beetles both require sufficient moisture to thrive. Obviously, as homeowners, we want the exact opposite. Both of those articles I linked to point out the importance of adequate crawlspace venting.
So, leave the vents open, insulated the floor, and make sure the vapor barrier is in great shape.