The single-neuron basis of cognitive processing in primates has mostly been studied in laboratory settings where movements are severely restricted. It is unclear, therefore, how natural movements might affect neural signatures of cognition in the brain. Moreover, studies in mice indicate that body movements, when measured, account for most of the neural dynamics in the cortex. To examine these issues, we recorded from single-neuron ensembles in the prefrontal cortex in moving monkeys performing a cognitive task and characterized eye, head and body movements using video tracking. Despite considerable trial-to-trial movement variability, single-neuron tuning could be precisely measured and decision signals accurately decoded on a single-trial basis. Creating or abolishing spontaneous movements through head restraint and task manipulations had no measurable impact on neural responses. However, encoding models showed that uninstructed movements explained as much neural variance as task variables, with most movements aligned to task events. These results demonstrate that cognitive signals in the cortex are robust to natural movements, but also that unmeasured movements are potential confounds in cognitive neurophysiology experiments.