We have been on 4 Christmas Market cruises and have loved them all. You never know what weather you will get. I take a small umbrella, fleece scarf, LLBean Gortex hiking boots with 1 inch rubber soles. warm socks, and fingerless gloves and a boiled wool hat. My husband's old cashmere l/s sweater and a wool vest over turtlenecks. This along with a lined raincoat get me thru any weather, layering as I see fit. You can judge the weather before you venture out. PM will always tell you the weather forecast. One thing you dont want is wet feet. Make sure boots/shoes are comfortable for walking over cobblestones and weather-proof. It can be rainy, snowy, and any combination thereof. It gets colder as the day goes on and if you walk back to the ship when the sun is hiding, you will be glad you wore your layers.
Enjoy, We hope to go on yet another Christmas Market. Loved the Seine trip so much, we are doing much the same trip next summer to see the same venues at a different time of year.