Yes, he may not be drinking when he's laying low for a shed- which is why it's so important to keep the humidity up even before they're in shed- by the time they're in shed, it's a bit late, other than misting & providing him a humid hide. BTW, the way the folds in his skin appear in the last photo is what suggests to me that he's going into shed- it can be very difficult to tell when you have a white or very pale snake- especially if you miss noticing their eyes being cloudy, but in gets easier with practice.
(Re 5* F.- I hope you were referring to the outdoor temperature, not in your house & where the snake is located?It's been a crazy winter for sure- I've seen MINUS 5*F. here- outside, of course. And not counting the wind chill factor.)