Clouds, if part of an optical communication channel, cause temporal widening and attenuation of optical pulse power. Space optical communication from satellite to earth (ground or airplane) occasionally involves clouds as part of the optical channel. Here, based upon Monte Carlo simulations, mathematical models are developed for the temporal characteristics of optical pulse propagation through clouds. These include temporal impulse response, transfer function, bandwidth, received energy and bode analysis. The method presented here can be used as an inclusive framework for developing other mathematical models of other characteristics of radiation propagating through clouds, as required. Several conclusions of this work are obtained. One is that simple prediction models can be applied to adaptive methods of optical communication. Another is that using shorter wavelengths such as 0.532 μm yields least temporal widening and maximum received power, and is thus preferable for optical communication. In addition, the simulation results strongly support the use of the double gamma function model to best describe optical pulse spread through clouds. This work is the first, to the best of the authors' knowledge, to present a comprehensive analysis of space optical communication through clouds.