There are poetry books containing letter poems written from one poet to another. If you look through letters you have written, or saved emails, you may find some that are worth salvaging as letter poems. If not, you might enjoy the challenge of writing letters with the dual purpose in mind.
Some poets write all their correspondence in poetic form.
A letter poem runs on, line into line, in a way that lends itself well to readings. Here is something similar to the form, but modernized, as it is obviously an email letter, also excerpted. It does not read much like a poem. It is 56 degrees here. I have the heat turned off as the chimney cover is being repaired and the chimney is covered with plastic in case of rain.