How about you read the FAQ, and then ask why no one can be bothered to answer your question?
I cannot see anything that explicitly addresses this in the FAQ page either. Indirectly though and related to this question, the FAQ page does show an animation of the Sun circling over a flat Earth. The extent of the daylight area due to the Sun does reach the circumference (or edge) of the flat Earth circular surface. That would mean the Antarctic is in daylight for 24 hours. As the Sun moves back north (radius of solar orbiting circle decreases) so the Antarctic region would be placed into 24 hour night. That corresponds to southern hemisphere winter.
What the animation does not account for though is the variation in the Suns altitude during a 24 hour period near for example the December solstice. In the animation the Sun follows a circular path and so its distance from the 'edge' of the flat Earth is constant. To an observer in Antarctica or near the SP region, that would mean they would see the Sun circle the horizon at constant altitude. That is not what is observed in reality. Perhaps there is another FE model which does account for this variation in solar altitude during a 24 hour period?
Something wrong with your explanation.
First that the Flat Earth's Sun never goes much further from the vertical over the Equator, so, for an observer over Antarctica, it will be far away always, never close by. Even for flat Earth model, the edge will be at 12738km from the center, or 6369km from the Equator, the Sun will be only at 4800km up (over the Equator), so, the observer angle for the closest Sun would be around 37° at Noon time and 14.1° at Midnight, hypotenuse will be 7975km at Noon and 19700km at Midnight.
Second, if the observer is with his back to the "ice wall" and facing towards the North Pole, he might see the Sun very low on horizon at some time, but the Sun will NOT circle the observer's back, right? To do so, the Sun would need to go outside the flat Earth model for a long distance, and keep close to the horizon on the observer's back. Imagine yourself sit over the public benches of a stadium, watching a game happening in the mid field, how some players would run around your back? Impossible, right? The game field is happening way over your front, the same as the Sun over the middle Equator of flat Earth model. So, the explanation doesn't work. I think you didn't understood, those pictures are a 360° composition during 24 hours time period, with the photographer rotating himself in a full circle, facing the Sun.