If you dream of writing a letter, it means you have something important to say. If you have an intuition which seems far-fetched, then you might prefer to write a letter, instead of telling it to your addressee.
Not every dream about writing a letter means you have important communication to convey. Sometimes, your inner consciousness panders to a whim of communicating to a long lost friend (or relative).
Dreaming of writing a letter to yourself can mean you wish to address issues which were ignored or neglected. Sometimes, you have unfinished business with your past. You want to speak up on injustice or something which you feel strongly about. You have no one to talk to, since this is a personal matter which can’t be easily understood by anyone. Dreaming of writing a letter is your brain’s innovation to try tackling this irritating matter of airing old issues.