Is there any basis for putting leather on top of a metal breastplate to protect from “the cold?” Or are they just setting up a means to disguise the fact that all of the extras are going to be wearing leather clothes in battle scenes instead of armor

None whatsoever. I think Benioff and Weiss wanted something to show that Sansa was being a good ruler when it came to military logistics, and just don’t understand that you don’t wear a breastplate against bare skin (which would be a problem in a frigid winter, I concede) but rather you wear a breastplate over quite thick padded jackets, which themselves are worn over one’s normal clothing, providing quite a bit of insulation from the cold.

Indeed, the one example I can think of of cloth being added on top of armor is the precise opposite of the climate of a Northern winter: namely the long cloaks and robes worn by crusader knights over their metal armor to shield it from the sun, so as to cut down on the serious problem of heat stroke and heat exhaustion that they faced wearing metal armor in the Levant.