The same reasons why many flightless birds continue to have feathers. First off they are excellent insulation. That could be critical for a not fully thermoregulated organism. Dinosaurs are thought to be warm-ish blooded but it's possible they didn't have the kind of thermoregulation that modern birds or mammals do.

Add to that waterproofing, which can aid in thermoregulation as well. The phrase "like water off a duck's back" is quite apt, feathers can shed water better than a modern high tech coat. Keeping dry means keeping warm. Also, dinosaurs that were occasionally aquatic could have benefited from feathers.

And very fast moving dinosaurs could have used feathers to aid in aerodynamics, which would allow them to run faster and maintain greater control over their movements.