A model has been developed which describes the hyperfine field at nonmagnetic impurities in ferromagnetic metallic hosts as arising from conduction-electron polarization. The problem is approached by considering the effect of both the screened electrostatic potential of the impurity and a spin-dependent potential arising from the exchange scattering of the conduction electrons at the localized magnetic moments of the host lattice. The influence of zero-point motion and thermal vibrations is explicitly taken into account. The model is applied to study the spin density at muons in Gd, Dy, Ni, Fe, and Co, and the predictions of the model are compared with experiment. The effect of various physical mechanisms on the temperature, pressure, and site dependence of the hyperfine field is discussed in detail.