This article describes in detail a technique for modeling cavity optomechanical field sensors. A magnetic or electric field induces a spatially varying stress across the sensor, which then induces a force on mechanical eigenmodes of the system. The force on each oscillator can then be determined from an overlap integral between magnetostrictive stress and the corresponding eigenmode, with the optomechanical coupling strength determining the ultimate resolution with which this force can be detected. Furthermore, an optomechanical magnetic field sensor is compared to other magnetic field sensors in terms of sensitivity and potential for miniaturization. It is shown that an optomechanical sensor can potentially outperform state-of-the-art magnetometers of similar size, in particular other sensors based on a magnetostrictive mechanism.