For the first time, to the best of our knowledge, optical cooling is demonstrated in a fiber at atmospheric pressure. Using a specialized slow-light fiber Bragg grating temperature sensor, -5.2  mK and -0.65  K were measured in a single-mode (1% YbF) and multimode (3% YbF) ZBLAN fiber with respective cooling efficiencies of 2.2% and 0.90%. Fitting a recently reported quantitative model of optical cooling in fibers to the measured temperature change dependence on the pump power per unit length validates the model and allows us to infer the fibers' absorptive loss and quenching lifetime, key parameters that are scarce in literature. These values are necessary for accurate cooling predictions and will aid in the development of fibers for application in optical coolers and radiation-balanced lasers.