If the temperature gets below 32 Fahrenheit (or even close), you should probably drain and/or winterize the water system (exact procedure depends on how involved your water system is). You mentioned 0 degrees, but unless you are measuring in celsius (unlikely) that is not freezing. 32 degrees Fahrenheit is the freezing point of water.
You could, alternatively, heat your garage, but that would probably be an added expense and worry all out of proportion to simply winterizing the trailer.
Think about sink drain hoses, water pumps, water tanks, and any other water hoses. Toilet and associated pumps and tanks (if you have one). Water heater (if you have one), and greywater tank (again, if you have one).
An A/C system could need winterizing - I'm not sure what you have.
Basically anything that has fluid or water in it.
is fine for over-wintering, although you might want to drain the lines and store the tank elsewhere, since you keep the trailer in your garage (Turn on stove and then shut off valve at tank and wait for burner to go out; then make sure to turn burner handle to off position.)
Raya (further south than you, and definitely still in winterizing territory)