A mid-infrared spectrometer consisting of a high power optical parametric oscillator, a frequency comb, and a cold ion trap is described and characterized. The idler frequency at 3 μm is measured accurately by analyzing the pump and signal beat frequencies with the comb. This is done via two spectrum analyzers, allowing for a wide and continuous scanning ideal for spectroscopy of cold molecules with unknown spectra. The potential of this approach is demonstrated by measuring a ro-vibrational line of CH(5)(+) in a 22-pole ion trap via action spectroscopy of only several thousand cold ions. The current setup limits the precision of the line center frequency determination to some 100 kHz with ample room for future improvements. Following this approach, ground state combination differences of molecular ions can be predicted in order to identify them in astronomical objects.