We present near-infrared photometric observations of 15 and spectroscopic observations of 38 cool white dwarfs (WDs). This is the largest near-infrared spectroscopic survey of cool WDs to date. Combining the Sloan Digital Sky Survey photometry and our near-infrared data, we perform a detailed model atmosphere analysis. The spectral energy distributions of our objects are explained fairly well by model atmospheres with temperatures ranging from 6300 K down to 4200 K. Two WDs show significant absorption in the infrared, and are best explained with mixed H/He atmosphere models. Based on the up-to-date model atmosphere calculations by Kowalski & Saumon, we find that the majority of the stars in our sample have hydrogen-rich atmospheres. We do not find any pure helium atmosphere WDs below 5000 K, and we find a trend of increasing hydrogen to helium ratio with decreasing temperature. These findings present an important challenge to understanding the spectral evolution of WDs.