Anonymous must be a big Friends fan...I was able to find a
transcript that includes your quote (is there anything that's not on the Internet?) and yes, the ice here is the kind you stand, or step, on, risking falling in.
Monica has already indicated to Chandler that she's upset about his ogling another woman. She then says the woman looks like her Aunt Marilyn, and Chandler promptly asks, in a halting way, if Aunt Marilyn will be at the wedding. Monica is barking out "Wafer-thin ice!" as shorthand for "You were already on thin ice with me, and it's getting thinner all the time!"