I'll be the one to say it, I think attempting a winter presidential traverse alone is foolish. In the summer, over the solstice, we started at 5:30 and finished at Pierce, coming down the Crawford Path at just before 9pm. Admittedly, it was a large group, but we were also able to stop at Washington to refill water.
You need to carry a foam pad, a stove, a -20 bag, and all the water you are going to drink. You'll have to hike at least two hours in the dark at the start, and at least four, but really more likely over five, at the end, basically from Monroe on.
There are ample spots where you won't have cell phone coverage, and to do that distance in a day, you would have to go without gear or clothing you should never be on the ridge without.
At the very least you need two hikers, and you need gear to allow you to survive being benighted.
The question is not whether you can do it under ideal conditions. The question is not even whether you can do it under less-than-ideal conditions. The question is what happens if something goes wrong. If you fall and break your arm, which is easy enough to conceive happening, are you going to have a bag to climb into and a stove to start, and are you going to be able to open said bag and start said stove with one arm only?
Just my two cents.
Brian