This is an interesting way to frame it, but then the obvious question is, for areas where it almost never gets above freezing, why doesn't the snow get infinitely thick?

The other main ways you lose snow are: sublimation, wind blowing it elsewhere, compaction, and getting dirty (darker color helps it melt in the sun). All of these are relevant for other cities in the snow.

> but then the obvious question is, for areas where it almost never gets above freezing, why doesn't the snow get infinitely thick?

this is how glaciers are created

snow getting stuck up, not melting, compressing by weight into much much smaller ice and then more stacking up. And during the last ice age this repeating for a very long time (because snow is mostly air, so the amount of ice you get from it is very little).

The reasons why this isn't too big of an issue on the north/south pool, Antarctica etc. is because this places are also very dry/don't have a lot of snow fall.

To have snowfall you need water in the air. Which mostly comes from heat evaporating water. This doesn't happen in non stop freezing cold places.

So the wind needs to carry the wet air over.

But there is a gradient between hot wet air places and very cold places. So a lot of water rains or snows off before reaching the places where snow doesn't melt.

A large part of the south pool is technically a desert as it has hardly any _new_ snow fall. Just a lot of years old snow getting moved around by wind.

It does, see: Antarctica

Compaction doesn't lose snow. It loses air. This causes the pile of snow to shorten.