Which saying is correct Walking on thin ice or treading on thin ice?
Walking and treading mean the same thing. The saying is actually
just "on thin ice" and it means you are standing on something that
might not support you. You say someone is "on thin ice" if they are
doing anything the might collapse at any second. If someone is
telling lies and is about to be found out, you could say they are
on thin ice.
I think it's also ok to say 'skating on thin ice'. Another
example of its usage (to add to what has already been said above)
is if someone is really trying their luck with someone who is at
the limits of their patience, they can be said to be skating on
thin ice, as the person could just snap.