When I run on the treadmill, I read. But I have found that the only way to read while on the treadmill is to hold the book, since it moves around too much on the stand, you move around too much. I've gotten very good at holding a book and running, which tends to screw up my neck a little bit.
Here's the acid test for appropriateness: Pretend that someone near and dear to you is witnessing what you are writing or sending, or knows what you are thinking about sending. If, say, your partner saw this behavior, how would he or she feel? That you are asking yourself this question could mean that you shouldn't be doing it!