We have a crawl space under the house, and while under there doing some maintenance the other day I noticed (because of the cold air pouring in) that there’s a vent from the outside. Yikes, we must be spending a fortune–like today when it’s 8 degrees F–'cause there’s a cold-enough-to-ice-up spot on the floor right over where that vent is.
You should be able to do so - my crawl space has vents with closable covers for this purpose. Open the vents up again in the spring to keep things nice and dry down there and cut down on home cooling costs.
Is there no insulation under the floor boards? There should be fiberglass, or a similar material, stuffed up between the joists. If that’s true the vents being open or closed should not make that big a difference.