Cutting edge wind predicition is of course done in textish mode, with a rotating slash/dash that varies in thickness. via
More text visualizations here.
ASCII-visualization of the current weather. Weatherspect by Robobunny (2003/2013) uses data from Wunderground and animates it in coloured ASCII. Snow, lightning, sleet and hail is supported, aswell as the sun and the moon. GIF made from this video by Mewbies.
A weather client that runs in the terminal: wego by schachmat.
h/t: svearikeslag
Environment Canada Weather Channel using the alphageometrical videotex protocol Telidon. From the mid 1980s. Thanks to Frederic Cambus for sharing.