Oh, I was thinking if you want to work from the ice, you can lay down some 4x8 foot sheets of plywood to help distribute weight in your working area. That will prevent you from falling through weak spots, and with ice underneath it will likely give you enough time to run off and with grip long before water becomes too deep. Another thought is some good snow shoes to distribute weight, though they would make getting back out rather difficult if you did fall through.
Example, I will go across a pond on x-country skis on some pretty thin ice that I would NEVER do on foot. An inch is enough with black ice, though I would prefer 2. On foot or skates, I prefer 4 or more inches.
Be safe!
Oh, and if you ever do fall through and get wet, strip naked and run for the nearest warm spot! Your wet cloths are your worst enemy. I think you may leave your underpants on but it may be a while before the jewels make an appearance again.
