Frosty I believe is an aberration, not a universal standard of what ice based person's view as their own mortality. Ice based life forms cannot shift their souls to outside objects, instead they house their souls in a single, cold, H20 Molecule that disappears when warmed.
I used to play sports in the summer, and hit Mcdonalds for $1 burgers on the Valu Meal with $1 any size drinks in the summer.