We use molecular dynamics simulations to study the behavior of supercooled water subject to different stimuli from a diluted azobenzene hydrophobic probe. When the molecular motor does not fold, it acts as a passive probe, modifying the structure of water around it, while when the motor is active, it induces elementary diffusion processes inside the medium acting mainly on the dynamics. We study two particular densities, the density of ambient water and a lower density around the ambient pressure ice density, chosen to favor high density liquid and low density liquid (LDL) water, respectively. We find that the passive probe induces ever an acceleration or a slowing down of the diffusion process around it depending on the density of water, while the active probe induces acceleration only. We find a crossover between the diffusion coefficients for the two densities near the passive probe, around T = 215 K. This dynamical crossover is associated with a modification of the structure of water near the probe. Structure calculations show a crossover of the proportion of LDL water around the same temperature, suggesting that it induces the observed dynamical crossover. In opposition with these results, the active stimuli increase diffusion for both densities and decrease the proportion of LDL water at low temperatures. However, we also find for the active stimuli a crossover of the LDL proportion between the two densities of study, showing remarkable similarities between active and passive stimulus results.