Since antiquity beeswax was used widely against chapped lips and mouth related issues. I've read limited sources claiming alum was also used.

There was a thread about this around two years ago.

Basically, they used other kinds of oils and rendered fats to moisturize chapped or cracked skins. Ointments would be prepared out of suet and beeswax, and "scented" with myrrh, marjoram, honey, and ginger.

Also, in Simon Schama's The Embarrassment of Riches: An interpretation of Dutch culture in the Golden Age, he describes the rich using olive oil or clove oil to sooth chapped or cracked lips, cheeks, and hands, while the poor would make do with linseed oil or lard. So what cosmetics or skincare products you would use seems to have varied considerably with social class.