PEX = polyethylene cross linked, it is the red pipe someone told you to use. The pipe does perform better in freezing weather but the fittings won't be expanding so will be the first to break from freezing.
Typical small diaphragm pumps will pull around 10' of head. Depending on ambient temps, the tank will start to freeze before anything inside. Using electrical heat tapes/gutter cable/tank heating pads and enclosing the tank with insulation will work if you have power available. Just insulating the tank will stave off freezing for a few hours. Recirculating water back into the tank will keep the tank water liquid until, probably, -15f. Installing a tank inside the cabin is easiest to deal with.
The other edge of this sword is how are you going to keep drain water liquid to dump? You may have liquid in the supply pipes but find that your drain tank is solid or break a drain pipe. In Georgia, these measures are less critical. In the Upper Midwest, a cold snap can get everything solid in hours.