How to keep pipes from freezing

I'm running water to an outbuilding behind my house. For the 25 feet from the
house to the outbuilding, I'll bury it below frost line to keep it from freezing.

Question - the last part of my house (before running it underground to
outbuilding) is an unheated garage (under a deck). It has a cement floor (thick
one). It would be a major,major pain to jackhammer that floor to run the pipe
under the garage floor. I was thinking about doing this - for that short
distance (15 feet), wrap heating coil around the water pipe, then put the
closed foam pipe insulation over that. Have a thermo-transducer in the
unheated garage. When temp drops below 32 deg, the heating coil kicks on.
Will this work? If so, I prefer to use PEX, but could the heating coil
theoretically melt through PEX (or dont they get that hot). The heating coil
wouldnt melt copper pipe ad copper pipe would probably transmit more
of the heat from the heating coil to the inside of the pipe than PEX, but if the
heating coil fails, copper bursts, PEX doesn't. Which should I use (please
dont say jackhammer the floor).

A little background on the project:

Is the water supply for year 'round? Hot and cold?
Where are you located? Or code specified depth for supply lines?

If you ran two pipes and then did recirculation, you might be able to get by without heat. If you lost power, neither might keep things from freezing.