Early in my career, I worked for the Federal Government. At one point, I was assigned to a team working with some Congressional staffers. One day during a break, I mentioned something about e-mailing my Congressman. The staffer told me, in his office at least, that was not a good idea. He said e-mails were simply scanned to see if they were pro- or anti- a particular issue and then filed. He said that people should always send a letter because 1) it spent more time in the staffers' hand as it required more effort to open, read and then file, but also 2) someone who was willing to take the time to write a letter, put it in an envelope, and invest the 40-some-odd cents it took to mail it was believed to be more likely to vote.
In the case of a company that has already made the decision to post signs prohibiting guns in their stores, a letter may be more effective than an e-mail in convincing the company's management that you (and the other people who will presumably send similar letters) are serious about changing your behavior and no longer patronizing their stores.