A method is developed to rank Forbush decreases (FDs) in the galactic cosmic ray radiation according to their expected impact on the ionization of the lower atmosphere. Then a Monte Carlo bootstrap-based statistical test is formulated to estimate the significance of the apparent response in physical and microphysical cloud parameters to FDs. The test is subsequently applied to one ground-based and three satellite-based data sets. Responses (>95%) to FDs are found in the following parameters of the analyzed data sets. AERONET: Ångström exponent (cloud condensation nuclei changes), SSM/I: liquid water content, International Satellite Cloud Climate Project (ISCCP): total, high, and middle, IR-detected clouds over the oceans, Moderate Resolution Imaging Spectroradiometer (MODIS): cloud effective emissivity, cloud optical thickness, liquid water, cloud fraction, liquid water path, and liquid cloud effective radius. Moreover, the responses in MODIS are found to correlate positively with the strength of the FDs, and the signs and magnitudes of the responses agree with model-based expectations. The effect is mainly seen in liquid clouds. An impact through changes in UV-driven photo chemistry is shown to be negligible and an impact via UV absorption in the stratosphere is found to have no effect on clouds. The total solar irradiance has a relative decrease in connection with FDs of the order of 10−3, which is too small to have a thermodynamic impact on timescales of a few days. The results demonstrate that there is a real influence of FDs on clouds probably through ions.