Fernando wanted me to look at this paper: How increasing CO2 leads to an increased negative greenhouse effect in Antarctica from Geophysical Research Letters. I glanced through it, and the argument seemed not crazy, so I decided to see if I could work out a model from first principles to see whether it could plausibly work. Think of it as a three reservoir problem in thermodynamics. Space is a nice cold reservoir, the central Antarctic plateau is also pretty cold (temperature Ta), and sometimes colder than the stratosphere (Ts). There is a greenhouse gas atmosphere lying between the stratosphere and the ground. Suppose the GHG concentration increases. In that case, radiative heat flow from the stratosphere to the surface will decrease. If the opacity increase is the same for downwelling stratospheric radiation and upwelling surface radiation, then the ordinary greenhouse effect will obtain. Suppose, though, that the GHG layer is more transparent to upwelling radiation than downwelling radiation. In that case we can have a reverse greenhouse.
But all the radiation involved is long wave, so how could that work? If the stratosphere emitted in somewhat narrow bands (little pressure broadening) and the GHG layer only absorbed in the CO2 bands (since hardly any H2O at super cold temps), then it might work, since the ice/snow are pretty infrared black and will emit broadband.
Note that this could only work for very special conditions.
It might be nice if somebody would check my work here. Rabett? Stoat?