I also had that idea to put spikes in my cycling shoes, I think it will work good.
I saw them in a shop where you can repair your shoes.
Currently I use continental top contact II winter tires and they are great in rolling resistance, but I have yet to put them to the test as this winter I had only one morning where the there roads were a bit icy.
I think the winter is cancelled here as it's currently above 10C and yesterday on the thermometer hanging outside in the sun it was 20C