Fat freezing, a treatment that can eliminate people’s fat cells, is becoming a hot new revenue opportunity for doctors’ offices and spas looking to capitalize on Americans’ willingness to open their wallets for a trimmer physique.Dermatology clinics and medical spas are increasingly offering a procedure called CoolSculpting to shrink love handles, flabby tummies and jiggly arms. Doctors’ offices are eager to offer the treatment because it represents a way to meet the fast-growing demand for fat-reduction services that don’t require surgery. It is also, they say, a way to get new types of customers in the door, including men. Revive Medical Spa, the cosmetic arm of a dermatology practice in Fayetteville, Ark., began offering CoolSculpting almost two years ago, after its owner, Dr. Lance Henry, decided it would meet his patients’ demand for nonsurgical fat reduction.Revive began with one CoolSculpting machine and added a second so clients could have two target areas treated at on...