The best replacement for snow storm is blizzard.

The best alternatives to snow storm are rated as following:
★★★★★  blizzard
★★  snowstorm
★★  ice storm
★  frost breath
★  snow storm
  crystal burst

Your alternative for snow storm is not listed? Suggest!
Speaking about snow storm, one probably shouldn't forget about lightning.

Other search terms related to snow storm and their ratings are:
★★★★★ lightning
You have in mind a companion for snow storm and it is not yet here? Propose!



Google Trends

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snow storm
blizzard
snowstorm