brian47 said:

Somebody mentioned reducing the pressures on snow or mud. That's not advisable because of what happens to the tyre at the bit that really matters, the bit in contact with the ground. The tread can start to go concave and the tread pattern can close up thereby reducing the efficiency of the tyre.
Proof that the tread of the tyre does actually go concave can be seen when a tyre which has been under-inflated wears the tread on both outside edges of the tread.
Tyres for normal vehicles should be operated at either the manufacturer's specified pressures or the pressure found by experimentation using a technique such as "the chalk test".
The myth about reducing the tyre pressure came about after those Icelandic off-roaders were seen doing just that on a snowfield, but if you check carefully the tyres are more like balloon type tyres with tractor tyre tread patterns which probably normally operate at pressures of 10 to 15 psi.

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jamesmartin said:

myth? military vehicles such as the dukw had adjustable tyre pressure system to cope with road and sand etc

though i wouldnt alter my tyre pressure for the little snow we get,running low pressure over distance on the road will kill your tyres but on sand etc low pressure gives a bigger foot print

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brian47 said:

In the case of military tyres, and those shown in your picture, that might hold true, but once again the tread pattern shown is more or less a variation on the tractor tyre tread.
Another factor which might or might not have some influence would be that the tyres on a DUKW would probably be cross ply whereas most road tyres these days are radial ply.
If the snow was so bad that I had to even consider going outside to let my tyres down, I'm pretty sure that I'd decide not to bother and go back to bed instead.

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