Per the normal rules, if you attack a firegiant with a frost brand in a sneak attack, you only double the cold damage. The logic is that the "physical" component isn't doubled. This is tied in to the same concept that you don't apply any weapon's special effects (wounding, poison, paralysis, etc) if no physical damage is applied.
I am in disagreement with the specifics of the rules and written and believe that by the spirit of the rules that if a firegiant is hit by a sneak attack ray of frost that since 100% of the damage is due to cold that the sneak attack counts as "cold" damage and gets multiplied as well.