We report on an ion trapping system for performing a novel form of cryogenic messenger spectroscopy with single molecule sensitivity. The system features a cryogenic radio-frequency ion trap loaded with single analyte molecules via a quadrupole mass filter. We demonstrate the ability to controllably attach inert gas particles to buffer gas cooled, trapped molecular ions. Sympathetic cooling by co-trapped, laser cooled 88Sr+ further reduces the translational temperature of trapped molecules to the millikelvin regime. We verify the presence of cryogenic "tags" via non-destructive optical mass spectrometry and selectively remove these adducts by resonantly driving vibrational transitions in the tagged molecular ions. This enables us to derive the vibrational spectrum of a single analyte molecule from the frequency dependence of the tag detachment rate. We have demonstrated these capabilities by measuring transitions in the C-H stretching region for single cationic fragments of both indole (C8H7N) and 1,3-benzodioxole (C6H4O2CH2). These capabilities are not reliant on a specific molecular level structure and thus constitute a general, non-destructive method for vibrational spectroscopy of individual molecular ions.