Individual variation in exoskeleton-augmented gait strategy may arise from differences in cognitive factors, e.g., ability to respond quickly to stimuli or complete tasks under divided attention. Gait strategy is defined as different approaches to achieving gait priorities (e.g., walking without falling) and is observed via changes in gait characteristics like normalized stride length or width. Changes indicate shifting priorities like increasing stability or coordination with an exoskeleton. Relationships between cognitive factors and exoskeleton gait characteristics were assessed. Cognitive factors were quantified using a modified Simon task and a speed achievement task on a self-paced treadmill with and without a secondary go/no-go task. Individuals with faster reaction times and decreased ability to maintain a given speed tended to prioritize coordination with an exoskeleton over gait stability. These correlations indicate relationships between cognitive factors and individual exoskeleton-augmented gait strategy that should be further investigated to understand variation in exoskeleton use.