My husband had chewing gum on a pair of his nice dress shoes. I suggested he try rubbing ice on the gum-it didn't work. Then I thought about using peanut butter. It worked! He rubbed the peanut butter on the gum, then with a paper towel continued to rub gently and the gum came off with the peanut butter!
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I always kept getting gum stuck on my shoe and on my kids' shoes. I have a 5 year old daughter who loves chewing gum and she just sticks it or throws it anywhere. So before leaving home or when you're home, before trying to remove gum on your shoes, take a small cube of ice, stick it or wipe it over the bubble gum before you pull it. This will not make a mess, it's easy to pull and neat.