Try cooking oil. If that fails, then you can ask the vet or groomer to use the clippers to get any that's on the hair. And then you would leave the rest to wear off.

To help remove gum from carpet, they freeze it with an ice-cube.

If you do that with the dog, be very careful not to touch the dog with the ice-cube in the process.

If the dog's hair has gotten mixed in with it, you may need to cut that part of its hair off. (It will grow back.)

Avoid using facbeook

Peanut butter, the oils in peanut butter break down gum and dogs love peanut butter so they can just lick it afterwards :p

Apply ice, peel it off.