In winter months, running outside can be rather interesting if you live in a snowy place. I find that snow and slush are fine, though I will often wear trail running shoes for better traction. But when it turns to ice, it can be really nice (and safer) to have some added grip. There are a variety of products on the market that can fit over your shoe that are designed to provide security walking or running on ice. I have used these but find them unenjoyable to run in. The have fallen off, and generally feel weird for running.
A few years ago I tried Icespikes. These are little screws that screw into a pair of shoes. It does mean that you have to devote a pair of running shoes to winter running, but I used an old pair and they have lasted a few years since I only need them a few times a year. (I am sure that one could unscrew the Icespikes, but that hasn’t appealed to me).
They have been very secure on ice, but they are small enough that I really don’t notice them much. They are pretty cheap and can last awhile – and would be my recommendation for running on ice.