If the epidermis is such a good barrier, how can cortisone easily travel through it?

cortisone is a lipid-soluble molecule hence can pass through the epidermis

Explanation:

Our adrenaline glands secrete various hormones including cortisol (also known as hydrocortisone) and corticosterone.

They belong to a group of steroid hormone bodies known as glucocorticoids and are used in a wide range of physiological processes such as inflammation regulation.

Pharmaceutical derivatives of these natural glucocorticoids include dexamethasone, fludrocortisone, prednisone, prednisolone, triamcinolone, which differ in strength. As all glucocorticoids have a similar effect, they all fall under the common name "cortisone".