The question as to whether or not the presence of warm hydrometeors in clouds may play a significant role in the nucleation of new ice particles has been debated for several decades. While the early works of Fukuta and Lee (1986) and Baker (1991) indicated that it might be irrelevant, the more recent study of Prabhakaran et al. (2020) suggested otherwise. In this work, we attempt to quantify the ice-nucleating potential using high-fidelity flow simulation techniques around a single hydrometeor and use favorable considerations to upscale the effects to a collective of ice particles in clouds. While we find that ice nucleation may be significantly enhanced in the vicinity of a warm hydrometeor and that the affected volume of air is much larger than previously estimated, it is unlikely that this effect alone causes the rapid enhancement of ice nucleation observed in some types of clouds, mainly due to the low initial volumetric ice concentration. Furthermore, it is demonstrated that the excess nucleation rate does not primarily depend on the rate at which cloud volume is sampled by the meteors' wakes but is rather limited by the exposure time of ice-nucleating particles to the wake, which is estimated to be of the order of few microseconds. ... mehrIt is suggested to further investigate this phenomenon by tracking the trajectories of ice-nucleating particles in order to obtain a parametrization which can be implemented into existing cloud models to investigate second-order effects such as ice enhancement after the onset of glaciation.