In the US, a seasonal ice runway has been operated for many years (with FAA approval) at Alton Bay in New Hampshire. I understand they look for 12 to 14 inches of ice to open but that's more to support the plow trucks than the aircraft. When I was flying on skis with a 7ECA we use to look for cars/trucks driving on the ice or more than 6". Comments above are correct, local conditions and knowledge matter more that a single minimum number of inches.
AOPA Online: Alton Bay ice runway opens