Infections produced by pre-symptomatic and asymptomatic (non-symptomatic) individuals have been identified as major drivers of COVID-19 transmission. Non-symptomatic individuals unaware of the infection risk they pose to others, may perceive themselves --and being perceived by others-- as not representing risk of infection. Yet many epidemiological models currently in use do not include a behavioral component, and do not address the potential consequences of risk misperception. To study the impact of behavioral adaptations to the perceived infection risk, we use a mathematical model that incorporates individuals' behavioral decisions based on a projection of the future system's state over a finite planning horizon. We found that individuals' risk misperception in the presence of asymptomatic individuals may increase or reduce the final epidemic size. Moreover, under behavioral response the impact of asymptomatic infections is modulated by symptomatic individuals' behavior. Finally, we found that there is an optimal planning horizon that minimizes the final epidemic size.