Wrapping alloy brifters for cold weather
Do you care about originality ?  Consider changing the brifters for something made from plastic or carbon because as you've noted, they don't suffer the same issue.  Likely to be an expensive solution.

So, can you paint your brifter's outside surfaces with an acrylic enamel paint?  you'll need many thin coats to build up a thick layer that won't abrade easily.  Sand between coats and add some clear coats as the top layer.  Avoid painting "under" the brake lever where it faces the gear change lever.

Instead of paint, you might choose to use a product called Plastidip, which historically was used for dipping tool handles, but more recently comes in a spray can and has been used for car wheel rims, etc.  This stuff comes in multiple colours.

You can also get sticky-backed cork tiles/sheet which is under 2mm thick.  Some creative pattern work and you should be able to put some heat-insulating cork between you and the cold bits.  Do apply sealant/varnish to the cork to protect it from the cold.

Leather is another valid alternative to cork.

Finally, you wear gloves already, so assume they are full-finger.  You could add heating wires to the gloves and run them off a small USB battery in your back pocket, or add heating wires to the brifters themselves and mount the battery on the bike frame.

If you do get a choice of colour, I'd suggest black, or as dark as possible to increase heat insolation from any sunlight.