How can I prevent a tankless propane on-demand water heater from freezing up in very cold climates?
Where is the tankless water heater to be located? If it is in a space that is heated, then freezing will not likely be a concern as there will be plenty of heat gain through the equipment enclosure.

If freezing is still a concern, look for a tankless unit that has a electric element for freeze protection. This will use a lot of energy if the unit is located in a cold garage, so best practice would be to locate the unit inside a heated space.