Well, if you close them off, you should make sure you have other ways to let in SOME ventilation, not sealing up all windows, etc., because it's just unhealthy and can even be dangerous (fumes from various things, fireplaces grabbing 02, etc.).

Close them off. As long as you have a moisture barrier down on the floor of the crawlspace and you are having no moisture problems, you do not need the vents open in the winter. My old house I sealed the crawlspace vents with foamboard cut to fit in the vents from the outside. Did that for 20 years without problems. I always opened it up in the summer as the ground water would come up under the plastic. In the winter it would dry out and I never had any problems. You will notice a difference in your heating bills as the crawlspce will stabilize at ground temperature if you have the exterior walls insulated.

Lucy, I'll keep your comments in mind as I do have a wood stove that uses fresh air from inside the house. My house is rather old though so I think there are enough other cracks where some fresh air can get in.

Rjoh, that's exactly what I had in mind. I'll give it a try this winter. I'll keep an eye out for moisture and make sure to remove the barriers in spring again.

Another thing to keep in mind when sealing off your crawl space is that you are risking Radon exposure. If you seal up the space without ventilation, then any gases in the soil has nowhere to go except through your house. Sealing the soil with plastic tarp and a fun under it is recommended according to the EPA, but I do not know the specifics on installation yet.

Here is the EPA's residential Radon page:
http://www.epa.gov/iaq/radon/pubs/consguid.html

Here is a link that might be useful: EPA & Radon

Not sure where you are, but here in North Carolina
I would never close those crawl-space vents. And yes!,
we do have a moisture barrier down. But this is in
fact Moist Carolina and I want as much ventilation
as I can get, both in the crawl space and in
the attic. I have tried closing both sets of vents
and have spent hours dealing with the result.

I live in ohio an the house had a double layer of 6 mil plastic down which cut off the moisture in the crawlspace. In the winter when it got below freezing the closed off crawlspace saved me worrying about frozen pipes and saved me money on heating bills. In a addtion my parents put on about 8-9 years ago the crawlspace has been sealed shut from day one. Dy as a bone under there. I was under it a week ago and found a screwdriver I left down there over a year ago. No rust whatsoever, and no moisture. If you live in a climate where it gets below freezing in the winter it is best to seal up the crawlspace.

I echo the story about North Carolina. We also keep our vents open year round. We only close off the one very close to the boiler in the winter.

But every climate is different.

DH all ways closes the vents to the crawl space for the winter. Reopen in the spring! he has some batts of insulation he uses over them after closing the baffles.
Never had water down there! Kathy G in MI

Already see moisture on the pastic over the siding