Cuts no ice

Does any body have the meaning to the phrase "cut's no ice"

"That doesn't cut any ice" means (to me) "that doesn't get the job done" or "that doesn't impress anyone." I couldn't find the phrase in any of my references but I'm guessing that it refers to the old-time custom, before refrigeration, of cutting blocks of ice from ponds and storing them in icehouses for summer.

So it's a phrase-synonym for "That dog can't hunt"?? Or "it doesn't cut the mustard"...
- Patty

That's what I think.