Use Ice Cubes and a Knife
After removing what you can with a dull knife or stick, put a few ice cubes into a plastic bag and press them against the gum. Leave it on there for about 45 minutes, and then once the gum is frozen, use the knife to scrape it off.
Spray With WD-40
Spray the gum with WD-40, let it sink in for a minute or two, and then try to wipe it all off with a paper towel. Repeat if necessary. If your shoes are cold and the gum is brittle, this method won’t work, so make sure the gum is nice and gooey.