I haven’t been to DLR/DCA in about a year, but from what I remember, the roaming characters usually do meet n greets in addition to their roaming antics.
The Mad Hatter can often be found roaming around near the teacups in Fantasyland. I have seen him riding the attraction (in character). Once he tried to order a cup of tea at the ice cream cart nearby. In the afternoon, he and Alice play musical chairs with kids near Refreshment Corner accompanied by the Main Street pianist. They’ll typically pose for photos with guests afterwards.
During Halloween season, Cruella can frequently be found on Main Street doing Meet n Greets, but she’ll wander off too (I saw her chase after the double decker bus shrieking about something last September).
Edit: I remembered some other roaming characters.
Tiana - she often rides the Mark Twain riverboat along with doing Meet n Greets near the Mark Twain dock on Rivers of American. I have had spontaneous interactions with her on the Mark Twain.
Gaston - During Halloween season, I have seen him out wandering the Matterhorn pass between the Hub and Fantasyland area. He’ll interact with guests stop and take photos if they are interested.
Mary Poppins and Bert - sometimes perform in front of Sleeping Beauty’s Castle in a small show. They can be found nearby the Hub interacting and taking photos with guests.
Additionally, the Fantasyland Band, will sometimes ride the carousel and play music as they ride. I have seen this on the weekends. I