Remember how you steered your "belly slam" snow sled? You simply deformed
the runners so that the leading portion took a new orientation. You can
find adult vehicles which turn without the (apparently difficult)
complication of a wheel/axle, simply by orienting sliding front skids. I
think some snow-mobiles may do this. Is this the rudder/keel effect adapted
to wheel-less land vehicles?
Perhaps beginning with an analysis of these "steering skid systems" would
give a fresh and easier start to grasping this "turning physics".