You can be on a river without it being frozen.Yes, many possibilities with on in at. What do you say f.i.when you are in a boat? On the river? At the river? Is a boat sailing on the sea or at sea? When talking of sailors one says: they are at sea? We say 'op zee', 'on sea.'(that's the confusing thing) The song says: Sailing on the river on a Sunday afternoon. But a sailor is at sea.