I have a pair of shoes which are very slippery on snow, ice and other smooth surfaces. I sometimes have the problem at home if the floor is wet. How can I make them less slippery or in other words - how to improve the friction of these shoes? I am interested in making them less slippery on ice and on other surfaces too.
You should wear in your shoes a bit. Walking on the smooth surfaces like ice does a little bit towards making the sole of your shoes less slippery as you understand, so you should walk more on the rough surfaces, like asphalt or something stony. Also you can rub thr soles of your shoes with something abrasive, like emery paper.
I have a pair of crocs and the rubber soles are extremely slippery on smooth surfaces, especially steel overbridges. I face even more trouble on wet tile floors.
However, one day by accident, I walked on a road (undergoing maintenance) with molten asphalt and that stuck to my soles real well. Ended up having some good traction on my shoes. Maybe if you could get your hands on some molten asphalt it could do the trick for you. Alternately, you could try some cement (Don't know about this one, just guessing)
Depending on your shoes, they can often be transformed with leather patches, or entirely new super grip soles that are designed specifically for the application you have in mind.
Your local, family-run, cleaning, key-cutting, shoe repair shop should be able to recommend something and help you with that.