I run 16 miles every Saturday no matter how cold it is. The only parts of my body that I found difficult to protect from the cold were my legs (decided about a year ago) and my arms. I have warm gloves (they are cool: https://www.amazon.com/gp/product/B008XM9SZU/ref=ppx_yo_dt_b_asin_title_o00__o00_s00?ie=UTF8&psc=1) but when the temperature drops below 20 or the wind blows, they are it not warm enough. There are products worn by runners that are better than regular gloves (these are called lobster claw gloves), but mittens are the best solution. Why? Because except for the thumb, all fingers are together to keep each other warm. (And every once in a while you can put your thumb in the main part of the glove and warm it up too.) These mittens are very warm and have been outside this winter in 18 degrees and a constant 20m/s wind. Even after spending the whole morning outside, my hands were fine.
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