No, the cold itself does not sap the charge by itself somehow. BUT a colder battery will be able to output less energy due to higher internal resistance (more energy lost to heat when discharging). Some cars bms are advanced enough to be aware of that and therfore display a smaller number.

• most North American solar installs are ac coupled

At least in Slovenia, and probably most of Europe, optimizers string inverters are used, so tapping to a dc line before the inverter is not that big of a deal