Interesting thread
There was a comment about the problem of maintenance of bicycles. But with so many other things, it is when you look at the modern variants. Something like this tend to keep working
http://en.wikipedia.org/wiki/Swedish_military_bicycle but it is sure not as fun to use as a more modern one. The royal guard regiment was just getting rid of them back in 1992. But there was still a few that we could borrow, to get to a supermarket nearby, if we had some free time.
They were used back in the days for infantry units, and they trained to be towed behind a tractor or a work horse. Basically the same tactics used by our northern brigades to tow infantry on skis during winter.
Might be a good option for infantry units working together with cavalry units.