I don't know that it's demonic 'dreams' really, but you know that dreams can echo what's going on around you. I remember blowing in my sister's face when we were little and she woke with a start and said she dreamt of a huge blowing wind!
My point is that I think when a demon seeks to scare and undermine a Christian, what better time when they are asleep and do not have a clear mind. I know of one pastor...a truly Godly man who would not make such a thing up; he said one night he woke from a bad dream and felt something on his chest, crushing him into the bed. He ordered the demon away with the blood of Christ, but in the morning he was covered with bruises.
Satan is real, demons are real and their hate for us is even more passionate then for the unsaved. As I said before, we don't want to go seeing demons in every event, but to not be aware that we have an enemy, and that enemy wants nothing more than our defeat and death, well, that's just giving Satan advantage. There is no doubt that demonic possession was seen in Jesus' day. Not of believers maybe, but we can easily see that Satan and his workers were at work. As far as Christian, ah, oppression went, Paul says that he was given a thorn, a messenger of Satan, which kept him from becoming conceited. We can also assume that the very great opposition that Christians did and do face may very well be demonically inspired.
Anyway, I think my point is that we should never assume that Satan does not do his very best to hinder and harm us. We may be saved, we may belong to another who is much more powerful, but I think that would just inspire him to hate us even more.