I'm not very keen on Game of Thrones as fiction, but the extreme variation of the climate reminds me very much of that of the planet Helliconia in the trilogy of the same name by Brian Aldiss.
Diagram of the orbital mechanics here.Helliconia lies in a loose binary star system, which consists of a yellow-orange dwarf similar to our sun, Batalix (spectral class G4), and a hotter and brighter white star, Freyr (Type A supergiant). Helliconia orbits Batalix, which in turn orbits Freyr. The Batalix-Freyr system is supposedly in the constellation of Ophiuchus, about a thousand light years from Earth.
Helliconia orbits Batalix in 480 days. [...] This is called the "small year". Helliconia and Batalix's orbit around Freyr, the "great year", is highly elliptical and takes approximately 1,825 small years which equates to some 2,592 Earth years. At periastron Batalix is 236 astronomical units from Freyr, whilst at apastron is 710 AU distant. [...] While seasonal changes in the small year are slighter than those of Earth, the long seasons of the great year are much more marked. When distant from Freyr, Batalix's illumination is sufficient only to maintain ice age conditions. However, Freyr's output is many times greater than Batalix's, so as Helliconia approaches Freyr, the tropics of Helliconia become hotter even than the tropics of Earth.
It's an interesting theory, and I could easily see where the seasons would be affected by a binary star system like that, but has there ever been a second sun mentioned in any of the books? I'm just finishing up the first one now so I'm not sure at present. The only near astral bodies that I know of are the one sun, the one moon and the moon that was destroyed in ancient times creating the first dragons.