Front wheel requires weight for traction: is this applicable to icy conditions? How is cornering on the road different than cornering on dirt?
Is cornering in snow any different?

I usually attempt to keep at least half my weight on the front wheel for stability when cornering and braking.
However, with all the ice this winter, I discovered that front tire slips are quite ordinary. Thus, I find it beneficial to keep my weight back, maybe only 20% on front wheel, and stay ready to dab in the event of front tire slip.
Is this reasonable behaviour on ice or am I being too scared and actually decreasing my stability by pulling back? Tires are Land Cruiser, saddle height is lower than typical XC to facilitate ... falling from not so high.
I'd look at which situations you are encountering tire slips in.  If you are encountering tire slips in cornering, studs are probably the way to go (or much more conservative riding).  If you are having trouble while you are braking, you may consider adjusting your technique to be much more rear brake heavy or rear brake alone.

I find that no matter what I do my pedal stroke is so sloppy and unbalanced that I almost never pedal on ice.  Generally I just try to coast over ice sections keeping my body as relaxed and centered as possible.  Major direction changes (without studs) are pretty much out as well.  I try to keep my weight off my handle bars so that I am not tempted to move the front wheel quickly or with any real force.  If you are going to try and turn the front wheel, it should be a feathered movement.  More than anything it takes practice and watching out for icy spots.  I probably fall (on ice) less than once a year now.  When I started riding in the winter (even with studs) years back it was probably closer to every other week.