When using some cold spell + Avatar of Fire + Cold to File, how does elemental damage modifieres work? Does it Apply to cold damage before convertion and to resulting converted fire damage? Or does it apply to only one element, and if so - does it apply before or after convertion?

When using some cold spell + Avatar of Fire + Cold to Fire, how does the elemental damage modifier work? Does it apply to cold damage before conversion and to resulting converted fire damage? Or does it apply to only one element, and if so - does it apply before or after conversion?