I've relied heavily on gore-tex style rain-proof outerwear for being outdoors in bad weather. Their breathability and water-resistance is miles ahead of dead animal skins.
First off, gore-tex is shit. But, yes, leather is nearly as non-breathable as a plastic bag that's why the traditional use of it is for things like elbow and knee patches, extreme heat protection, such things. Boots, of course. The solution is as always proper layering, not exactly a modern invention: You wear something breathable for warmth, and something non-breathable that you can take off, and has breathing flaps (rain doesn't fall from below), for water protection.
Do you have experience with those? Especially the breathability to waters resistance ratio is much worse in all plant-based leathers I have tried. Would love to find a good alternative!