Solar storms are blocked by the Earth's magnetic field and "funnelled through" the magnetic poles into the air. The auroras may be extended further away from the poles and can cause power blackouts when they interfere with electricity distribution systems. But don't change surface weather systems much.
The influence of a solar wind on weather is very important, contrary to prevailing opinions in meteorology. The main mechanism of coupling suggested by researchers studying the electrodynamics of the Earth system is the modification of a global atmospheric electrical circuit and the activation of condensation nuclei in clouds. A thorough review of the problem is presented by Tinsley (2000).
(INFLUENCE OF SOLAR WIND ON THE GLOBAL ELECTRIC CIRCUIT, AND INFERRED EFFECTS ON CLOUD MICROPHYSICS, TEMPERATURE, AND DYNAMICS IN THE TROPOSPHERE, a copy of the article is attached)
According to a back-of-the-envelope calculations, these effects are important for explaining large-scale cloud systems. I also wonder if the forecast of the major weather systems can be improved after the inclusion of electrodynamic effects?
Another article by Voiculescu et al (2013) (Clouds blown by the solar wind) provides experimental data linking cloud cover and solar wind.
The entire problem of linking the solar wind and the weather has only recently attracted the attention from the meteorological community and we can expect some genuinely new results very soon.