There are different types of warnings: Perl-warnings and other warnings. I think you should never see Perl-warnings in production for multiple reasons:

• variables used without initialisation or declaration, accessing non-existent array cells; this will undoubtedly cause unreliable output
• security concerns: warnings might reveal more than you want in case security is an issue

Of course, there are other, non-Perl errors, like "Disk is almost full". These messages should be logged to a file and regularly inspected. I would not use "warn" for this.

Back to your question: I use strict in production, and depending on the type of application and its audience (general audience: no, expert audience: yes) warnings.