Nope. No mail at all. One character even says something along the lines of: everyone knew by the end that if you wanted to get rid of a dead body, you should send it to the post office because you'd never see it again. This character was thirty, but spoke of 'the end' as if it was ages ago.

Yes, the mail coaches were still running in Lords and Ladies, which was 6 years ago, and in Hogfather which was about 5.