We present phase-resolved near-infrared photometry and spectroscopy of the classical nova (CN) V1500 Cyg to explore whether cyclotron emission is present in this system. While the spectroscopy do not indicate the presence of discrete cyclotron harmonic emission, the light curves suggest that a sizable fraction of its near-infrared fluxes are due to this component. The light curves of V1500 Cyg appear to remain dominated by emission from the heated face of the secondary star in this system. We have used infrared spectroscopy and photometry to search for other potential magnetic systems among old CNe. We have found that the infrared light curves of V1974 Cyg superficially resemble those of V1500 Cyg, suggesting a highly irradiated companion. The old novae V446 Her and QV Vul have light curves with large amplitude variations like those seen in polars, suggesting they might have magnetic primaries. We extract photometry for 79 old novae from the Two Micron All Sky Survey Point Source Catalog and use those data to derive the mean, un-reddened infrared colors of quiescent novae. We also extract WISE data for these objects and find that 45 of them were detected. Surprisingly, a number of these systems were detected in the WISE 22 μm band. While two of those objects produced significant dust shells (V705 Cas and V445 Pup), the others did not. It appears that line emission from their ionized ejected shells is the most likely explanation for those detections.