If you have a working 120v heater in the wet bay, draining the tank isn't necessary. If you don't have any working heat source to the wet bay, you might try putting one or two 60 watt light bulbs in the wet bay plugged in to add heat. Make sure the compartment is as air tight as possible.
If it isn't too much trouble draining the tank isn't a bad idea but the other piping in the wet bay needs the heat as much or more than the gray water tank does.
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Michael and Georgia Day
1992 Newell 43.5' #281
8V92 DDEC-2, HT740
PT Cruiser GT with Remco Transmission Pump https://newellowner.com/newell-photos/