Click on the link. It says, under each of these photos, "Boat." (Not ship. Boat.) When there's open water, these ice boats can sail on the water, too. LOL!
That is indeed a boat. DN iceboats can go up to 80 mph. I know several hardcore DN ice boaters here in Michigan.
(ETA: When there is open water, an iceboat's steel runner blades would probably sink it.)
To answer the OP, you can sail in a regular boat in the winter. But a sailboat is typically hauled out and stored for the winter. Even if it was stored on your property, you'd still take a lot of important things off of it which wouldn't be put back on until springtime fitting out. It would say something about your characters that they have this boat ready to hop on and sail in the dead of winter: either they never bothered to store it properly in the fall, or they're rather wealthy and have, say, a heated outbuilding they just leave the boat in with all its gear intact.
Why yes, I do work in the marine industry.