Snow and ice build-up can shift the SWR curve of an antenna to a lower frequency. It is relatively rare in most parts of the country, so it isn't something that many of us need to worry about. The snow or ice clinging to the radiator is behaving like a dielectric coating, but the SWR shift will disappear after the antenna warms and the ice or compacted snow melts or sublimates.
Typically, falling or drifting snow that piles up at or over the feedpoint and base of the vertical has little or no effect on antenna efficiency, tuning or SWR.