The point here seems to be that the circle linking the two sundogs almost exactly touches the horizon. Since it is a so-called
22 degree halo, the Sun is approx. 11° above the local horizon.
Now if this is South pole station, which it seems to be, there are two dates on which the Sun ha that elevation:
22 October and
20 February.
I'd prefer the first date, as that would be a nice birthday present for me
.
And, kelfazin, thanks for the South Pole tip!