We examine the effects of a relativistic wind on the spin-down of a neutron star and apply our results to the study of soft gamma repeaters (SGRs), which are thought to be neutron stars with magnetic fields greater than 1014 G. We derive a spin-down formula that includes torques from both dipole radiation and episodic or continuous particle winds. We find that if SGR 1806-20 puts out a continuous particle wind of 1037 ergs s-1, then the pulsar age is consistent with that of the supernova remnant, but the derived surface dipole magnetic field is only 3x1013 G, in the range of normal radio pulsars. If instead the particle wind flows are episodic with small duty cycle, then the observed period derivatives imply magnetar-strength fields, while still allowing characteristic ages within a factor of 2 of the estimated supernova remnant age. Close monitoring of the periods of SGRs will allow us to establish or place limits on the wind duty cycle and thus the magnetic field and age of the neutron star.