It really is whatever you want or need it to be. The use of the D before the relationship initial has been around forums for as long as I can remember and is very universally used on internet forums. I do think that the original use was intended to be Dear or Darling and the fact that Disney starts with D is just a convenient coincidence. You will also see many posts that will lead you to realize that the D probably stands for "Dumb" or "Damn", "Disgusting" or a whole host of other things!
I really don't even "read" them as Dear Husband or Dear Daughter etc anymore, I just see that whole as meaning husband or daughter. I have been on internet forums for a VERY long time!