I've not heard of there being a Protect Ring in the snowfield area. All the items I know of are:
-) Added Cut (NT Mod, changed to Sneak Attack): From the mountain area, use the top-right path
-) All Materia: Inside cave in the pseudo-world map snow area (the one where landmarks can be used)
-) Safety Bit: Inside central cave of Map, after passing the jumping block puzzle
-) Potion (NT Mod, changed to Ether): Screen before ice floe jumping puzzle
-) Elixir: Far left area of Map, inside a small cave
-) Mind Source (NT Mod, changed to T/S Bomb): Forest area