If the holder is hit by a Ice-type damaging move, it consumes the Snowball and its Attack is increased by one stage.
It does not activate if the holder already has +6 Attack stat stages (unless its Ability is Contrary, in which case it will not activate if the holder has -6 Attack stat stages). It does not activate if the holder is protected from or unaffected by the Ice-type move (e.g. due to Telepathy or Wonder Guard).
If multiple Pokémon each holding a Snowball are hit by an Ice-type move at once, each hit Pokémon will consume its Snowball before Symbiosis transfers any item (including Snowballs).