So what OP is missing is the central limit theorem[1]. According to which any sum diatribution of independently-identically-distributed random variables in the limit becomes gaussian distributed.

So taking it apart, given some restrictions, any sum of randomly distributed data is gaussian distributed.

If you take an average of some value. E.g. sea ice extent at fixed date x, e.g. January 1st every year, you have a sum distribution.

So you're not talking about the random distribution of any date, but of the random distribution of the average value. Only this has the Gaussian distribution.

Now there are some restrictions IID - independently identically distributed. This is the part the quants got wrong. Identical distribution is usually not the issue, we can, for a certain timespan, assume that the random distribution stays roughly the same.

But independent was the issue. If one event is correlated with the next, the central limit theorem may hold for a bit, but if the correlation is, too extreme will break down, like in the quant models of yore.

Their estimates for the housing market risk were ok as long as the credit defaults were not highly correlated, but as soon as the crisis started some vicious cycles formed between the foreclosures and tumbling house prices causing more foreclosures.

The models broke down.

Back to the ice sheats, if we assume the melting of the ice sheats won't increase (or decrease) the melting of the ice sheats we're good. I don't know about causative mechanisms here, but it could be that the models do break down in these times of extreme change.

That doesn't mean that the extreme change is nothing to worry about, since only by being extreme might it break the models.

[1] https://en.m.wikipedia.org/wiki/Central_limit_theorem