If you are going to wear leather hats a lot in the summer, you need either a thick head of hair, or need to add some insulation so the hot leather doesn't lay on your bald head. I often switch to a straw hat on hot sunny days. Winter can be a problem too. Frozen leather on a bald head is not too comfortable.
Some of this depends on the hat style. If there is no air gap between a bald head and the leather, the effects are really intensified. I wear an Aussie style hat, low profile; the top rests on my head, so I can tell you current weather conditions! I have at times folded a handkerchief and laid it on the the top of my head to prevent migraine headaches and heat stroke.
Felt cowboy hats can be problematic in the summer too. There is good reason to have a selection of hats for the seasons. That selection may include a straw hat, a felt or leather hat, and for cold winter climates (<0C or 32F) something with ear flaps to protect your ears, as well as being able to protect your bald head.
Then there's a picture of a cowboy out on a snowy windswept range with a bandana wrapped around his hat and ears. Dual purpose, keep the hat from flying away, and keep his ears from freezing.