We present broad-band multiwavelength observations of GRB 080310 at redshift z= 2.43. This burst was bright and long-lived, and unusual in having extensive optical and near-infrared (IR) follow-up during the prompt phase. Using these data we attempt to simultaneously model the gamma-ray, X-ray, optical and IR emission using a series of prompt pulses and an afterglow component. Initial attempts to extrapolate the high-energy model directly to lower energies for each pulse reveal that a spectral break is required between the optical regime and 0.3 keV to avoid overpredicting the optical flux. We demonstrate that afterglow emission alone is insufficient to describe all morphology seen in the optical and IR data. Allowing the prompt component to dominate the early-time optical and IR and permitting each pulse to have an independent low-energy spectral indices we produce an alternative scenario which better describes the optical light curve. This, however, does not describe the spectral shape of GRB 080310 at early times. The fit statistics for the prompt- and afterglow-dominated models are nearly identical making it difficult to favour either. However one enduring result is that both models require a low-energy spectral index consistent with self-absorption for at least some of the pulses identified in the high-energy emission model.