One-year-old Merlin was shot on the bottom of his stomach last weekend.
His owners Margaret and Ray Astle, of Sussex Drive, Kidsgrove, say they are appalled at what has happened.
Mrs Astle, who is a Staffordshire county councillor for Kidsgrove and Talke, said: "At first I thought he had caught a chill in the snow because he seemed a bit lifeless and was sleeping a lot.
"I was absolutely horrified when the vet examined him and said he had been shot.
"I don't know who would want to do such a thing to an animal.
"It's just lucky we took him to the vets when we did."
Mrs Astle is offering a £50 reward for anyone who comes forward with information about who shot her cat.
Anyone with information is asked to contact Kidsgrove police station on 0300 123 4455.