Unsupported ice should be at least 10 centimetres (4 inches); supported ice such as that in artificial rinks can be much less, as little as 1 centimetre (1/2 inch)
Probably about 5' - 10' depending on your height. But I could imagine you'd have a hard time moving in ice. I think you might die trying this actually.
The skates melt under your body weight the ice just a little bit to form a thin water film. In other words, the skates glide on a very small water cushion.