You'll be fine. A wipe down with a soapy wash cloth and a little water works fine for basic cleaning. (Wet Wipes work really well, too.) Only do dishes once a day, with just a little hot water and soap. Be conservative about lights and furnace, pile blankets on the bed and use those battery powered push on / off lights. My showers are really quick things - rinse, turn the water off to soap up, then rinse again. Done in under 5 minutes, and that includes washing and conditioning my hair. I use a french press for coffee. The kettle boiling on the stove helps warm the trailer up first thing in the morning.
I can be out for a week with my 30 gallon fresh tank and my portable 100 watt solar panel. My big limitation is the grey water tank. It's little. I pour my dish water down the toilet into the black water tank to extend my time between dump trips.