This reads more like a discussion question/request for help brainstorming than a specific question about worldbuilding. I'm pretty in GOT if pressed the answer would be magic more than anything else.

An impact event can cause #3 and #2 to certain extent. #1 will be more tricky.

I don't see how Nan's words imply a hundred feet of snow falling in one go. It could just as easily imply snow accumulating to a hundred feet deep.

@KlausÆ.Mogensen or indeed (almost) non-stop snow for 6 months - both "in one go" and "accumulating"

A nearly tidally locked planet? But even if possible , the darkness light cycles would be predictable.

note that "little children are born and live and die all in darkness" wasn't all that uncommon in earlier times. infant mortality, probably especially in cold winters, was high.

My understanding is that Martin has clearly stated that the winters/seasons are due to magic. He posits no astronomical phenomena capable of these conditions. No one else has either. 100ft of snow is equivalent to 240 inches of rainfall, something like x4 or x5 that record monsoons produce.

Even 100 feet over a few years would present extreme logistical challenges for survival. My vote is on Nan exaggerating juuuust a bit.

The causes of the super-seasons are clearly magical and tied to two locations: summer/heat/fire associated with the doom of Valyria, the smoking sea, and dragons; and winter associated with the Others and the far north beyond the Wall. There's a reason it's called "A Song of Ice and Fire": the causes of the super-seasons are the fundamental mystery behind the whole thing.

Does this answer your question? What natural phenomenon could lead to greatly varying season lengths?

@JoinJBHonCodidact Not quite; it's supposed to be a one-time kind of thing, hence the asteroid impact or volcanic eruption as a possible cause. It's not "all the seasons vary wildly in length"; it's "we have normal seasons...and then this one REALLY nasty winter".

exceptionally long winter that's a part of a recurring cycle of seasons

@JoinJBHonCodidact "It's NOT supposed to be a regular but exceptionally long winter that's a part of a recurring cycle of seasons"

How does this happen in a world with dragons, resurrection, face-swapping assassins, icy zombies, and a wall of ice hundreds of feet high? Pretty easily, I'd guess.

100 feet of snow over a winter lasting a year or more is not unreasonable. Several places on earth achieve snowfall rates comparable, albeit in winters of only a few months. Crater Lake Oregon averages 43 feet of snow in a winter. The Japanese ski resort of Niseko averages 50 feet of snow per winter. Japan overall is very snowy. Of course mostly because of winds that cross open water from the continent. As for varying winter lengths, see astronomical answers

This is UNCLEAR. (a) This appears to have nothing at all to do with Game of Thrones, which is muddying the water considerably. (b) It appears that you're taking the normal winter period and asking how to make that period as cold as possible. (c) You don't seem to realize that the colder the temperature, the less likely snow will fall. So what you specifically mean by "nasty" is incredibly important.

And if by "nasty" you mean lots and lots of snow (and not really, really cold temperatures), then you need to realize that there must be humidity to have snow. That means evaporation, somewhere....

@ARogueAnt. No - I'm trying to figure out what a one-time event that could cause this would be. It's not supposed to be a regular occurrence.

Ahh, fair enough, close-vote retracted. There are similar questions relating to volcanic winter, asteroid winter, nuclear winter - but none as far as I can see that are exact duplicates now. The trouble is, now you've added that criterion, you've invalidated all the existing answers.