Mice in little wagons

If you have ever wondered how young boys entertained themselves in the twelfth century, the contemporary Yorkshire chronicler William of Newburgh gives a clue. In his list of the many sins of Roger, archbishop of York, comes this:

"Instead of selecting persons of eminence, with whom (as though with jewels) the church of York had formerly glittered, he conferred benefices on striplings, or even boys still under discipline of their masters, better calculated from their age to build up childish houses, to yoke mice in little wagons, to play together indiscriminately, and to ride on it long reed, than to sustain the character of dignitaries in the church."

I'm afraid I can't elucidiate what 'to ride on it long reed' means, and google doesn't help. Any ideas?