From your description it sounds like you may be ok to utilize the fresh water tank. In order to do so you will need to de-winterize. However, with temps around freezing, at night and even during the day, you will need to run the heater to keeps things thawed inside.
I cold weather camp quite often. Some things you may want to consider.
Don't de winterize just yet. Its only a weekend trip and you say you don't plan on using the tap. So get yourself a couple of 5 gallon water jugs and keep them in the bathtub.
Buy a bottle or two of RV antifreeze and bag of water softener salt.
When you urinate, put a cup of the water softener salt in the toilet first. Do your business and flush it utilizing enough of the water from the water jugs and add half cup of RV antifreeze.
When you defecate, fill the bowl with water, add a cup of RV anti freeze and once done flush, rinse if necessary (remember add RV anti freeze).
Don't forget to pre fill your black tank if a gallon or two and your toilet chemicals and a couple cups of RV antifreeze.
I have done this routine religiously, while doing December hunts in temps as low at 30 below zero. I leave my TT winterized and I keep all the water inside in a 35 gallon container and a couple 5 gallon jugs. I utilize a couple extra 20lb propane tanks and leave a Buddy heater as my main heat source during the day while I am out, and during the night. I run main onboard heater with the generator in the evenings until we go to bed. (this keeps the batteries charged and heats the TT more efficiently.)
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