Pretty sure the roads will still be closed, though I'm not sure where the gates are located when accessing the lake from the north side, which is lower in elevation and may not have any snow at all right now. The best plan is to check with the ASNF Black Mesa Ranger District before you go.
Black Mesa Ranger Districts
P.O. Box 968 Overgaard, AZ 85933
Voice: (928) 535-7300