There are two sets of seasonal cycles, one predictable and weak and the other variable and strong.
The weak annual cycle has given Westeros enough annual seasonal variation that crops can grow in the temperate area from Highgarden to the Neck. It's probable the axis is less tilted than Earth's, but without some kind of season there could be no apples or wheat. In the North, there is not enough summer to notice, and in Dorne not enough winter to notice. (It's been calculated that the planet is 10% bigger than Earth, and the Wall is probably around the Arctic Circle.) So climate tends to be strongly associated with latitude. Characters talk about "the year of the false spring" and so on but this is not helpful, since ocean currents also can change climate from year to year.
The strong variable cycle, whatever the mechanism, brings colder temperatures overall. Summers are mentioned but don't seem to bother anyone or are considered the norm. Because even the Maesters can't predict winters, it's likely that there is no cycle at all. None of the theories out there can explain it:
---A second sun would work, but none has been mentioned. Possibly the sun orbits a dark dwarf---but even if it can't be seen, you'd think someone would have calculated its influence by now.
---A wobble in the axis could work, but people would notice when the stars move.
---The sun could be unstable.