Many of these weather conditions only have nouns to describe them, such as blizzard, tornado, hurricane. So if it is happening now, you can only say, "There is a blizzard" or you can use "we are having," as in, "we are having a snowstorm."
Words like rain and snow can also be verbs, so "it is raining/snowing" is correct.
Some weather words can be used in adjective form, as in "it is windy" "it is sunny" "it is rainy today."
Hope this helped!