Highs in both Kyoto and Tokyo are likely to be in the 40s Fahrenheit, with snow possible but not likely. (It snows only every few years.)

For a Minnesotan like me, this means a wool coat or a lightly padded jacket, a hat for windy days, and lightweight leather gloves. No snowshoes, ski pants, face masks, or other Arctic survival gear required. I don't switch to my next level of warmth unless the high for the day is below about 20°F (-5°C). Daytime highs of less than 0°F (That's about -20°C--yes, it happens in Minnesota) require a whole new level of gear, but I can guarantee that you will not find such temperatures in either Kyoto or Tokyo.

My one piece of advice is to wear thick socks. You have to take off your shoes to go inside temples, and I once made the mistake of wearing thin socks to visit a temple in February. I was chilled through and could not warm up until I got into the bath that evening.