Yes, they do. A blog post on the National Geographic website describes the results of a study about how blind people dream.(1) The participants who were born blind did not report any visual impressions. Among those who previously had sight, the number of visual impressions reported decreased with the time since loss of sight.
Just as there are many ways to take in the world, there are many ways
to dream about it. Blind people dream, just as they live, with a rich
mix of sensory information.
About 18 percent of the blind participants (both congenital and
later-onset) reported tasting in at least one dream, compared with 7
percent of controls. Nearly 30 percent of the blind reported smelling
in at least one dream, compared with 15 percent of controls. Almost 70
percent of the blind reported a touch sensation, compared to 45
percent of controls. And 86 percent of the blind reported hearing,
compared with 64 percent of controls.
Despite these sensory differences, the emotional and thematic content
of dreams isn’t much different in the blind and the sighted. Both
groups reported about the same number of social interactions,
successes, and failures in their dreams. They had the same
distribution of emotions, and the same level of bizarreness.