[Autumn]

I think a good argument to be had here on this is that Firebird's feather tiles are expendable so they end up dealing full damage, ice tiles are pretty much the same way and you need to apply the debuff to begin with (Passing a status infliction check with either 10/15 LV Frostbite, or 50 with Intensify Cold, or 30 with a very specific youkai ability)

I see no reason that feathers exist the way they are but frostbitten targets have to have the damage split when pushed across ice tiles.