Don't put out any outgoing mail. Even if yours is dry it will get wet when it comes in contact with other mail that is wet.
If you can hold off sending a letter in the rain do so
If it's raining the wet letters get tossed into a bucket, then into a larger hamper than into a machine for sorting.
Wet letters make other dry letters wet. So even if you take them to the post office they may encounter wet letters in their way.
Ink runs.
Although I have had Canadians tell me that their postman does not pick up outgoing mail. Thats what I thought. DUH!2
Don't put out any outgoing mail. Even if yours is dry it will get wet when it comes in contact with other mail that is wet.
If you can hold off sending a letter in the rain do so