Yes, ice is most definitely composed of energy, too.
I think you’re getting tripped up by the fact that we always describe positive heat transport as hot to cold. It’s perfectly acceptable to describe negative heat transport from cold to hot, it’s just not the convention.
For example, it’s easy to picture heat (energy) from the environment warming a cold can of soda. Now just picture the negative as cold propagating out from the can and cooling the immediate surroundings. Both are energy transport, one positive, one negative.
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