I am not sure if you are asking as a general rule or if it was plowed in the last day or so, but it used to be plowed fairly regularly - enough to get 3-5 cars in there easily. I have been in there 4-5 times in the winter in the past without any problems.
I plan on spotting a car there in the next few days, then drive down to Long Lake for a trek on the N-P back to Lake Placid. I just was not sure if they plowed it during the winter.