The LEDs are diodes, Gadge, and hence don't normally have any issues being connected to AC, in my experience. Of course they are only conducting half the time, so it would be a neat trick to wire one headlight in the forward current direction and the other in the backward current direction, but I don't see any other problems. I haven't actually done it with high power LEDs like these, but LEDs are quite fast-switching, and have a decent Peak Inverse Voltage rating like most silicon diodes, so I'd expect it to work.
However, Iceman's lights look like incandescent filament ones anyway.
