In this paper, we propose a novel signal processing method for road surface roughness classification exclusively from wheel speed sensor signals. Road surface quality has a significant impact on fuel consumption and driving safety. Traditionally, it has been measured using specially equipped vehicles and, more recently, shared via cloud-based infrastructure; however, such data can be unavailable or quickly become outdated, making onboard solutions essential. We analyzed a large wheel speed sensor dataset from various test maneuvers to determine how road surface roughness influences spectral characteristics under different conditions, including changes in speed, tire pressure, payload, and tire type. The proposed road surface roughness classifier uses only wheel speed sensor signals. It selects signal segments appropriate for processing based on driving conditions and computes their order spectra. The number and relative power of the spectral peaks within the identified interval of interest of the order spectrum are related to road surface roughness. The implemented classifier is capable of distinguishing between rough and smooth road surfaces based on the number of peaks in the interval of interest. The overall accuracy of the implemented road surface roughness classifier was 87.4%.