It can be challenging dealing with Raynauds in cold climates. I have found keeping my whole body warm helps, including hat, scarf, and gloves. I also have gloves in many weights depending on the season. In addition, in the extremely cold weather, I used thin wool liners under heavy mittens. There are also hand warmers you can purchase if you are outside for any length of time. For severe cases, medications can help.
Hope this helps a bit,