Recent observations of the trade-wind regions highlight the covariability between cold-pool properties and mesoscale cloud organization. Given the covariability of organization with cloud cover and albedo, this suggests a potential impact of cold pools on the cloud radiative effect (CRE). To explore this, we use an ensemble of 103 large-domain, high-resolution, large-eddy simulations and investigate how the variability in cold pools is determined by large-scale external cloud-controlling factors (CCFs) and shaped by processes within the mesoscale. It is demonstrated that the size and frequency of occurrence of cold pools are strongly influenced by the near-surface horizontal wind speed and large-scale subsidence. The temporal evolution of cold pools is strongly correlated with the diurnality in radiation. Even without external variability, we find a strong intermittent behaviour in the evolution of cold pools, governed by a complex interplay between cold pools and clouds which expresses itself in the form of shallow squall lines. These squall lines result from precipitating downdrafts, cold pool outflows and the resulting gust fronts, reinforcing parent clouds. Cold pools influence the CRE of trade cumuli, but only when they exist during the day. This emphasizes the importance of the synchronization between cold-pool events and the diurnal cycle of external CCFs for the dependence of the CRE on cold pools.