In fact, polygonal ground is more complex than you think. The length-scale of the polygons is related to the skin-depth of the warming and related change in volume. From measuring the size of the polygons, you obtain estimates of the thermal skin depth and consequently the time-scale over which these changes operate.

Annual freeze-Thaw leads, typically, to metre-scale polygons. Century to millenia climate cycles lead to 10-100m polygons

Obviously, the freeze/thaw of water is the most powerful volume change (~10%), but even simple thermal expansion and contraction of wholly solid materials is also capable of developing polygonal cracks. There are a number of publications available on this topic.

On Earth, freeze thaw IS the dominant mechanism, but it isn't the only one.

Do not make the simplistic step of assuming that because there are polygons on Mars, there is also freeze/thaw on Mars.

There *may* be freeze/thaw cycles on Mars, or the polygons *may* be due to solid-state processes. Don't leap to a hasty conclusion - let's see what Phoenix has to tell us about the nature of the ice and various other things, then we can think about martian near-polar conditions. Some modelling needs to be done on the rate of polygon formation by various processes, and the efficiency of wiping out small meteor craters, but not destroying dunes. There are some answers buried in there, if we ask the right questions and don't jump to "obvious" answers.