It wouldn't need to do anything but "ping", the battery could last for years. You could even have a mechanism to disable it when the lines are repainted, though normally roads that use the existing version of these reflectors would have them removed when moving lines.

The transmitter would have to be powerful enough to go through a small amount of snow in some states.

The question is can we get the car companies to agree on a standard for this? Would it make sense to put it in the frequency range allocated for vehicle radar systems?

What we get instead is an attempt to define the whole system de jure, including full V2V protocols and specifications.