The Eleventh Doctor cited text messages as a method of communication. (TV: The Power of Three)
The Eighth Doctor felt that intonation, as in speech, was conveyed in a text message with "those little faces" and via "amusing punctuation". When he asked Liv Chenka how Tania Bell "sounded" in a text communication, Liv had him look for himself. They both agreed that her tone was stern. (AUDIO: Dead Time)
On 26 March 2005, (PROSE: Operation Mannequin, The Doctor Was Involved in the Dummy Massacre) during the Dummy Massacre, TERI_LOVER tried to text while on the London Eye, believing they were going to die. (PROSE: Dummy Massacre)