Various dictionaries disagree.
Webster's:
2season
verb: to make (wood) ready for use by slowly drying it
Dictionary.com:
verb(used with object)
11. to mature, ripen, or condition by exposure to suitable conditions or treatment: a writer seasoned by experience.
12. to dry or otherwise treat (lumber)
Anyways, yes your wood still dries, but more slowly. I imagine it dries especially slower if you live in an area that gets a lot of snow. Even when its freezing down here, there's rarely any snow, so my stack are still fully exposed to sun and wind. If your stacks are buried in snow and ice for months at a time, that may effect the seasoning process more than just cold weather.
The problem with that definition visa vis firewood is as follows: if one were to take a cord of dry, ready-to-burn wood and submerge it in a lake till it reached maximum saturation, that wood does not become "green" again. It becomes wet, seasoned wood.