Shane, winter is quite a different ballgame. If it is a drought year like last year, it
might be possible to zip up and back in a day if you have perfect weather. However, after any significant amount of snow, it becomes nearly impossible.
People will hike the Mountaineers Route in spring, but that is a mountaineering route, and guiding services take groups up that way regularly. It always involves an overnight.
The other issue is that last year, Inyo County put up a gate on the road down low, so it adds about 3 miles and 2k in elevation, just to get to the trail head.
Here are several threads to read:
Whitney Main Trail in Winter? So, you want to climb the Mountaineer's Route in winter? 
