If the ground is wet, a waterproof mat can help you stay drier. If it is raining, a waterproof mat will be wet to lie on. Might be slippery, too.
No harm in using a mat for any prone deliberate shooting, Just gets in the way for position shooting.
Ziplock bags are your friends, for scorecards, notebook, etc.
You need something to keep your ammunition dry. Having a chamois handy is useful. Plastic tubes (pieces of vapour barrier, etc.) can be elastic banded to your scope to keep rain off the lenses.
In your other thread, you were asking about shooting jackets. Few competitors use them. Something with a bit of elbow protection is useful. Something to reduce the butt slipping on the shoulder is also not a bad idea. In SR, you often have to get into position and shoot quickly. Whatever you wear has to be comfortable, and not reduce freedom of movement.
A jacket could be used in sniper. Once again, some do, most don't.
I have experimented with an old 10X cloth coat. Very light, some padding. Usable, no benefit I could see for SR, probably no harm in sniper.