You are right that heat is energy, more specifically it is the kinetic energy of the particles. Cold air has slower moving particles than hot air. This means cold air is denser than walm. However importantly the cold air is still moving and still has energy.
Wind comes from cooler, denser air filling in the gap left by walm air as it rises. Think of a mushroom cloud, very hot air risers and the cooler air fills up the gap left.
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