When will storms yet to come close the road? It is too soon to know. What are you willing and able to deal with on your hike if you end up being able to drive to the trailhead? Much of that area is pretty mellow terrain, but it is too soon to know what you may be facing. Pleasant weather that week and weekend would make reaching Cottonwood Lakes reasonable for most who would consider late November High Sierra backpacking, but heading up something steep and shaded by terrain (like Old Army Pass) could be a much different story. I'd check weather.gov point forecasts, whitneyportalstore webcam, and mammothweather.com the second half of this month leading up to a trip and have backup plans. Nearby, Death Valley NP is often great that time of year.
Aside from currently melting snow, conditions look likely to be mild for awhile: