There are three approaches that can remove your thirst during winter:
Firstly, if you can find a thermos flask that fits a standard bottle cage, it might actually be large enough inside to contain so much water that it removes your thirst.
The main problem is that market for such bike-compatible bottles would be very small, so you can't probably find such a bottle. The easiest way to make a thermos flask compatible might be to buy a normal (thin enough) thermos flask and somehow make an adapter around it. Perhaps by 3D printing and gluing, perhaps by making it out of wood, perhaps by some other manufacturing method. If you really want to cheap out, you could just make the adapter from a wrapping of duct tape around the thermos flask and then wrap a string at the correct location to make it thinner like bike bottles are thinner at some location to keep them stable in the cage. You won't be able to drink while moving, though, because most thermos flasks aren't designed for quick drinking but rather keeping contents cold or warm, but that shouldn't be a problem. It's perfectly acceptable to stop for a drink.
Secondly, you could fill a standard bottle with warm/hot water and then insulate the bottle around with thick clothes. That should keep the contents warm. There's no need to drink continuously, so if you for example find that the time you have to drink is an hour from starting the ride, test with various thicknesses of insulating clothing and various temperatures of water to reach at optimal insulation and optimal temperature so that the water is drinkable when you need to drink it. This, too, will not allow continuously drinking while moving, but you rather have to stop for a drink to be able to remove the insulating clothing around the bottle, but that shouldn't be a problem since there's no need to drink every minute, you can perfectly stop for a larger drink every hour.
Thirdly, you could of course replace the water bottle with a credit card. I'd say most cyclists are near enough a grocery store at least during some parts of their ride, so while thirsty and convenient, stop at a grocery store and you can find something to drink.