chains

You still drop your tyre pressures but not as much.

I.E. Typical road pressure in my car is 32 psi , drop them to 24 with chains.

You don't want chains to cut into good rubber when you hit a hard patch.

Dropping to far can cause chains to flay / come loose.

Note talking bush driving not on Bitumen at a resort , where it can be more important for narrow chain to cut ice and pressures usually kept as were.

Reducing tyre pressures is fine with chains fitted as long as you reduce your speed acordingly. Probably wouldn't drop them too much on a light duty road tyre but have found no ill effect on quality mud terrains even down as low as 8 PSI.
Cheers Craig...........

You will find that driving up and back from the ski fields normal pressures are fine (that is if you have to fit chains).

Track driving can be a different matter, as lower pressure can help with floating over snow.