Welcome, James.
Unfortunately almost nobody attempts Mt Whitney in December after as much snow as we have received. Due to the snow conditions, there is no way you could climb to the summit in a day.
It sounds like you are getting the opportunity to come this way for a first time, so you could take advantage by just driving up and scoping out the area. Drive up Whitney Portal road as far as possible. Sometimes there is a locked gate, other times it is "soft closed" -- a road closed sign that some people drive around. If it is hard closed, you could get a flavor of the trail by hiking up the road through the snow to the trail head. And if you have time, go up the trail a bit more.
You could also do what others do in winter -- visit Death Valley. As suggested above, find the road to Telescope Peak, and maybe climb it. Or just tour Death Valley -- you could spend several days seeing what is available.
