That old pile of brake and shifter cables found the reason for their continued existence today. My first version of the cables utilized a daisy chain of sorts, wrapping the cables around the rim. After spending a good amount of time perfecting the weave so it laid snugly between the knobs, but still proud enough to grab the ice, I realized such a design would only be more trouble than it was worth should I get a flat. A respectable chain solution needs to be quickly and easily removable. The design I settled on is something similar to auto chains, though simplified in its lacing. The pic here shows the final product. It could probably use at least twice as many laces, but as a prototype it should do fine.
2 72" lengths of shifter/brake cable
30 6" lengths of brake cable
32 wire terminators
Surely there is a better solution than these wire terminators for joining the lengths, but as a first go it's quick and simple.
Using the wire terminators shown here, I laced the 6" lengths together in a zigzag pattern. The guide wire which provides the tension for the chains will run through the eye of the terminator.
With the 30 6" lengths laced together, they can be slipped onto the shifter cables, which serve as the guide wire for the chains. One end of the guide wire is terminated by the shifter bead, the other is capped with the remaining wire terminators. The best way to do this is to run the free end through the same eye that keeps the bead, then add the terminator. Tension can be kept on the system by snugging the terminated ends of the guide wires toward each other, which means that the guide wires should be threaded in opposite directions.
To cinch up the cables and keep them from slapping the frame I tied the cables down with zip-ties. Though this defeats the purpose of making a removable chain system it's also a point for which there should be a simple solution. I haven't tested these off road yet, won't do that till I get rid of the zip-ties. An absurd amount of salt was dumped on the road today, so I didn't get a good test of their bite, but there should be a good freeze this week - more on that later.