The game's loading screen and Word of God by Gaider years ago confirm that Dwarves do dream, but not in the Fade.
Dwarves do not enter the Fade when they dream, yes. This doesn't mean they are barred from the Fade (as is evident from the fact that a demon can force them in), they simply do not go there naturally.
The phrasing is of course quite clear. If one was to say they don't dream at all, one would say "Dwarves don't dream at all."
Even Oghren had a dream in Awakening that wasn't a Warden dream, and he has a freak-out at the notion of being in the Fade later on -- which ends up saying that dreaming is natural for Oghren and Dwarves. Going to The Fade is going to freak him and any other Dwarf the hell out, dream or no.
Which makes subsequent games "DWARVES DON'T DREAM AT ALL" strike me as a crock and retcon.
It's not really clear if the Dwarf Wardens are in the Fade as they dream of all that Taint-like goodness with the Archdemon. The landscape and atmosphere looks the part, to be sure, but it's pointed out that what the Wardens have is a connection to the Archdemon and Darkspawn hive-mind, and we haven't really seen anything to indicate that the Darkspawn hold a connection to the Fade far as I can recall -- given that their magic draws itself from the Taint in their blood and Demons know nothing about Darkspawn/The Taint other then what they might see in dreams.