Related, may I ask in what climatic area are you living? Where I live it gets so cold in the winter that I almost can't even wash my hands with cold water.
On the other side I feel like in the summer I could take on such a habit. Maybe a solution would be to warm it just slightly in the winter.
Hands are also the hardest part of the body to cold-shock, all those little bones and large surface area. People who routinely go into ice baths often keep their hands above the water so they can stay in longer.