Screw your shoes and run through the winter
The big secret to running in winter snow and ice is screwing your shoes. It's easy and turns your shoes into tank treads. Never worry about slipping again.
The 3/8" is the perfect length for just about any running shoe. The shorter screws work okay but tend to fall out much quicker. Using anything longer will lead you into ouchie territory.
Also note that the screws with zinc coating are a little more expensive but they won't rust as quickly. You can get very cheap versions of this screw but they will rust after the first run.
Lastly, notice that slot across the top for a flat-blade screw driver. You may think, that since you will use a hex screw bit that you don't need it and can buy some screws that are just flat, don't do it. Go with the screw pictured below and in the video. It has a lip around the edge and that slot greatly increases grip. I bought screws one winter that didn't have the screw driver slot across the top and they weren't nearly as grippy.
BTW (Winter 2018), I have been buying these screws in packs of 100 for years. I just found a pack of 1000 for $28 on Amazon. That's a huge savings and should last me years into the future.