I don't think there is a good way to winterize the water pump and still run city water. The pump is right next to the furnace, so it's not real vulnerable anyway.
If you are just staying in the trailer,
- close the valve for the ice maker under the sink.
- disconnect the tubing at both ends (at valve and at solenoid) and blow it out.
- You can reconnect it then for later use, but leave the valve off.
- Finally disconnect the lower connection at the solenoid and let the water drain out of the solenoid* and ice maker line.
- reconnect that line as well - ready for use when you are.
*NOTE -that white wire wrapped around the line and solenoid is heat trace, so as long as the fridge is running there isn't much risk on that part freezing anyway, but I would drain it.