Executing an important decision can be as easy as moving a mouse cursor or reaching towards the preferred option with a hand. But would we decide differently if choosing required walking a few steps towards an option? More generally, is our preference invariant to the means and motor costs of reporting it? Previous research demonstrated that asymmetric motor costs can nudge the decision-maker towards a less costly option. However, virtually all traditional decision-making theories predict that increasing motor costs symmetrically for all options should not affect choice in any way. This prediction is disputed by the theory of embodied cognition, which suggests that motor behavior is an integral part of cognitive processes, and that motor costs can affect our choices. In this registered report, we investigated whether varying motor costs can affect response dynamics and the final choices in an intertemporal choice task: choosing between a readily available small reward and a larger but delayed reward. Our study compared choices reported by moving a computer mouse cursor towards the preferred option with the choices executed via a more motor costly walking procedure. First, we investigated whether relative values of the intertemporal choice options affect walking trajectories in the same way as they affect mouse cursor dynamics. Second, we tested a hypothesis that, in the walking condition, increased motor costs of a preference reversal would decrease the number of changes-of-mind and therefore increase the proportion of impulsive, smaller-but-sooner choices. We confirmed the hypothesis that walking trajectories reflect covert dynamics of decision making, and rejected the hypothesis that increased motor costs of responding affect decisions in an intertemporal choice task. Overall, this study contributes to the empirical basis enabling the decision-making theories to address the complex interplay between cognitive and motor processes.