You should be fine, but you will likely want to run some type of heat. Before the kids, we used to camp well into December in the northeast. Temps it in the upper 20s at night shouldn't cause any freezing, as it should get above freezing during the day.
Regardless, open cabinet doors with water pipes underneath to make sure that heat migrates towards the pipes. Invest in a $20 electric heater and place it on your counter, that will work wonders towards making the camper more comfortable. A pleasant side effect is that the electric heat will dry out the air a little, taking away some (but not all) condensation issues with cold weather camping.
Have fun!