Concern with Breakage of Acrylic vs Glass vs Polycarbonate: 
The impact strength of Acrylic is 0.4 ft lbs/inch.  The impact strength of tempered glass is very dependent on the geometry of the object impacting the glass as well as the edge condition of the glass, so maybe there is no such “property” of glass to compare to. Nonetheless, it is much easier to break glass than acrylic. Some people claim acrylic is roughly 10 times tougher than glass. This test for all materials is usually done at room temperature. Generally acrylic mirror is usable from -40 up to + 65 deg C (-40 up to 150 deg F). What happens is that the impact strength of the acrylic drops off at low temperatures, and below – 40F the material becomes very brittle. By comparison polycarbonate has an impact strength of 18 ft lbs/in which is about 45 times more than acrylic. However, its impact strength decreases below -20 deg C. I do not know what the impact strength of either material is at – 40 deg C. The maximum use temperature of PC is higher than that of acrylic, but in practice that may not help much with mirrors because prolonged exposure above 65 C (150 F) is going to damage the back coating of the mirror so we would not recommend any higher use temperature for either polymer.

What is the Thermal Conductivity of the Glass, Acrylic & Polycarbonate: 
Acrylic is about 0.19, where PC is about 0.2 and glass is about 0.8. Unit of measure is W/m degK. So glass is about 4 times more thermally conductive than either acrylic or PC.

Using a Back Side Heater on Plastics:
    We have customers who routinely use back side heaters on vehicle mirrors very successfully. However your application might not be the same. For one thing you are talking about defrosting at – 40 deg C. Our customers do not test for that and in most end use cases never see that extreme cold. Secondly, post-forming a mirror with thickness of only about 2 mm or roughly 0.080 inch. In other applications we could be using 0.236 inch or 6 mm thickness, which is three times thicker than “normal”. With the thicker plastic (of low thermal conductivity) and the lower extreme temperature, this might be the achilles heel which kills the deal for acrylic or PC and forces someone to use stainless steel or glass. Frankly the only way to know is to test it.

Mitigating factors or other design ideas:
    In Europe a lot of plastic mirror is used outdoors for roadways, even in Scandinavia. One strategy employed there is to back-fill the cavity with a phase-change material that releases heat when solidified. You can choose phase change material that melts/solidifies at some design temperature, perhaps 5 deg C, and rely on the heat being released during solidification to keep the mirror continuously defrosted. Periodically (overnight for example) the mirror would need to be warmed back up to remelt the phase change material. This may not be practical in your application but outdoors in Europe it works pretty well because the sun comes out and warms up the mirrors during the daytime.