Two ice cubes and a woollen hat

Correct!

Wool does not have a heating effect. It just has a very good isolating effect due to its structure. Therefore, it keeps the ice cube cold, and your head warm in the winter. The reason for that is that the thermal conductivity of the material (wool) is very small. The heat transport effects are very small. Therefore, only a very small amount of energy from the environment is transferred to the ice cube. Materials with these characteristics are called isolators.

You can try this yourself. Take two ice cubes of equal size. Wrap one of them in wool and keep the other one just like that. Of course, you can also put one of the cubes into your woollen hat, but be careful. The hat will be wet in the end. Now observe, which one of the cubes melts faster.
Isn't that remarkable?