Charge induced changes in homogeneous freezing rates of water have been proposed to constitute a possible link between the global atmospheric electric circuit and cloud microphysics and thus climate. We report here on high precision measurements of the homogeneous nucleation rate of charged, electro-dynamically levitated single water droplets as a function of their surface charge. No evidence has been found that the homogeneous volume specific ice nucleation rate of supercooled microdroplets is influenced by surface charges in the range between +/-200 elementary charges per μm(2). It has also been suggested that filamentation in highly electrified liquids can induce freezing at temperatures well above the homogeneous freezing limit. We report here the observation of Coulomb instabilities of highly charged droplets that are accompanied with the formation and ejection of fine filaments from the liquid supercooled droplets. Down to temperatures of 240 K, which is close to the homogeneous freezing limit of uncharged water, no filamentation induced freezing has been detected. At even lower temperatures, the droplets froze before the instability was reached. These findings rule out that filamentation exerts an important influence on ice formation in supercooled water. Combining these findings, we conclude that the surface charges (even at their maximum possible density) have no significant effect on the homogeneous ice nucleation rate of supercooled cloud droplets.