Thought I'd pass along this link for what appears to be an upgraded version of an AutoSock (in addition to cloth, it also has rubber traction pads with embedded steel spikes to further increase ice traction). Looks like they run about $25 more than the Auto Sock ($125 total).
http://www.snobootz.com/howitworks.php
Edit: Looks like only a couple of sizes are $125... the correct size for the Ax would be $310!![]()