Mike133, welcome.
There is a guy (Richard P) who hiked Whitney every week over a year's time. ...only he almost died his last trip, caught near the summit, overnight, in a storm.
That said, it all depends on the type of winter weather we are having. In a wet year, forget it. You could be breaking through several feet of snow, while trying to stay on the trail. Or going up the mountaineers route, doing a steep ascent against several feet of snow that could cut loose in an avalanche.
In a dry year, like the guy who hiked every week, you have a fair chance. But if there is more than a 6" covering of snow, which is highly likely, December and January are pretty much out of the question. The energy level required to break trail through snow like that, on top of the distance and elevation, makes the effort super-human. However, currently there has only been a dusting of snow, so people are making it to the summit so far this fall.
I am assuming your adventure club hired a local guide service (SMI comes to mind), or else some in the group were highly skilled winter mountaineers. You should contact a guide service if you are serious. But even the guides call a trip if weather or conditions are not good.
Given your experience, you would be better to wait until next year. Guides take people up the MR in March and April. In May, you need a permit, and snow covers the trail, so going up that is more difficult. But by then, snow is consolidated and melting, so people make it if they camp overnight part way up. Once the snow melts enough so that the cables section is manageable, (usually sometime in June), it becomes a day hike possibility. But you need to get a permit -- lottery starts in February -- or try for an online grab of a cancelled or no-show permit.
Climbing Mt Whitney is a great experience -- don't let your enthusiasm fade. You can do it, just maybe not in December. Good luck!!
