During the winter months, it can feel like it's harder to get going in the cold. While it is true that a cold muscle cannot perform as well as a warm muscle, when you are running in cold conditions, your muscles are generally warm and warmed to performance level. Cold exposure will reduce blood flow to your skin to help preserve body temperature, but circulation to muscles isn't impacted in normal exercise circumstances.
If you stop moving and/or if you aren't dressed properly, your body core will start to cool, and your muscles will contract rapidly (shiver) to produce heat. You would have to be pretty cold (hypothermic) to reduce blood flow to the muscles, and in that situation, running performance would not be your issue.
Can you run as fast in the cold? Properly dressed means you will be wearing layers, which will create drag and added weight, both of which will slow you down.
Traction in the cold is another issue. Even when there is no snow or ice, your footwear will be stiffer from the effects of cold on the shoe materials. This could slow you down. If there is snow and/or ice, the traction will be at its worst around the freezing mark and improve as the temperature drops, especially when it drops below zero.