B&A: Geeky question regarding Game of Thrones?

Well you are going to need to get a bit geekier...

The most obvious mistake in your thinking is that the planet would be closer to Sun at some points and further at other points. It is not the distance to the Sun that dictates seasons but the tilt of the rotational axis that causes the seasons. So because the Earth's rotational axis is by and large a constant as the Earth moves around the Sun our seasons have a relatively constant length over the time it takes Earth to move around the Sun.

So there would have to be something that caused the rotational axis of the SoFaI's planet to behave oddly.

One can account for the seasons by looking to the "3 Body Problem" which describes how chaotic motion such as the strangeness of the the SoFaI's seasons (If you have read the series you no doubt no that the length of the seasons are not always the same) might arise.

"Specific solutions to the three-body problem result in chaotic motion with no obvious sign of a repetitious path"

But there is nothing in SoFaI to make one believe that the Moon is anything other than roughly analogous to Earth's Moon.

So...one theory might be how the mass of the moon in SoFaI is itself somehow chaotic and aside from from really powerful magic there is no "real world" explanation that suffices.