I have been doing some cross training (biking) and I have found the cold on the feet is much worse than running. I bike much faster than I run, and the air coming into my shoes is very cold on my feet.
I have run a few experiments.
First, I applied duct tape to the front uppers of an old pair of running shoes. I do not much care that the shoes are not in the best conditions for running as I am not hitting the ground with my feet. This cut out the wind considerablely, and allowed me to go longer before my feet were too cold to continue.
Second, I tried changing my sock part way through the ride. This also proved helpful, but not as helpful as I had expected. The inside of the shoes were already wet from the sweat and so the socks be came wet fairly quickly.
My most recent experiment was to take Ezheat had warmers and active two of them and duct tape them to the top front of my old shoes. I put each in a plastic bag so the tape would stick to the plastic back and not the warmer. The once I have are about 2 x 3 inches. The are a liquid in a pouch with a small metal disk about the size of a penny. When you flex the disk, the supersaturated solution crystallized and in a few seconds produce a temperature of about 130 deg F (55 deg C) which last for 30 – 60 minutes.
In my initial test it was about –1 C. The warmers produced comfortable heat even through my shoes and I could feel this warming though 80 min of biking. I began to sense cold in my toes about 60 min but could still feel heat at the mid point of the foot.
They weigh about 900 grams once they have been used they can be “recharged” by placing them in a cloth and dropping them in boiling water for about 10 min. The Crystals go back to liquid and they can be reactivated by snapping the disk again.
I have found them on the internet and at a local store. They seem to retail for about 5 to 6 dollars each. I purchased my at Lee Valley Tools here in Ottawa where they sell for just about $6.50 each or $5.50 if you buy four or more. I bought 4. My plan is to start two and tape them on my shoes and then when the stop being effective to active the other two which I will care inside my jacket. And replace the expended ones on my shoes and see how that works to keep my feet warm for the whole time I am out.
I am not affiliated with Lee Valley, but they have outlets across Canada and so may be a local source for other crazy Canuks who run in our winters.