Those aren't trench coats, they've over coats to keep the wind and to some degree, the rain off you. A friend of mine has a modernised trench coat with treated leather and Nomex, on top of that it's easy to wash so it pretty much slicks off any crap that comes it's way and is hard-wearing and somewhat fire-proof.
If you went anywhere near a fire in one of those wool overcoats, you'd be immolated immediately.