Register your Public CD-Key on
LORE. If you're not sure what that is, look
here.
Once you've done that, find any character page,
Acacea's for example, and click "Send Letter" at the top. Then you just select the character who will be sending it and write the message. It deducts 50gp from your bank account and is automatically signed unless you select the "anonymous" option for an additional 100gp.
And yes! It's a great system.
If you haven't seen it already, check out the quill and parchments for being able to write notes and letters in-game...likely helpful for a mute character.