Ridden Clydesdales at county level are generally turned out as normal horses, not in 'heavy' gear, though I spotted some shaved docks at the RHS ridden Clydesdale class, because the same horses were doing the heavy horse classes later in the day! Some are pulled and plaited, others have longer manes loose. There are probably pics avaialble on line somewhere (possibly even on here?).
I have seen a small clydesdale turrned out and shown as a heavyweight hunter - it didn't look too out of place, but wan't a very typey clydesdale - I had to ask, as I thought it was part bred.
I have also seen ridden clydesdales in riding club horse classes locally - not sure that they could be considered suitable for all riding club activities though?