Lip balm for winter rides?

After over 125 miles this past weekend, my lips are chapped to hell and a little painful.

I do sometimes suffer from dry lips, and the weather makes it worse. I carry a tube of Carmex in one of my pockets – it was good over the summer, but isn’t coping well with this weather – I think it’s too thin and doesn’t last.

Any recommendations please?

(Believe it or not, in previous years I’ve used cheap lip gloss and can’t recall having this problem.)