I have yet to ride with one (nor my children) but lately (possibly due to the YoaMD theme) I have seen characters on rides with kids every time I have been to the park. The last trip, in April, I saw Mickey and Goofy on a Jungle Cruise boat. I saw Donald on the Dumbo ride. We also spotted Alice and the Mad Hatter on the double decker bus. Chip & Dale on King Arthurs too. So they are doing it, but you're right, I hadn't seen it for a long time before our trip last November.
within the past few months i've seen micky on the rockets with a kid and peter pan, wendy, pluto, geppeto, and foul fellow on autopia. it was quite a show to see the 5 of them marching out from backstage right up the exit and onto the ride. the kids didn't know what had just happend or why they were all together.