The best replacement for snowstorm is snow storm.

The best alternatives to snowstorm are rated as following:
★★★★★  snow storm
★★  blizzard
★  snowstorm

Your alternative for snowstorm is not listed? Suggest!
Speaking about snowstorm, one probably shouldn't forget about thunder.

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



Google Trends

Scale is based on the average worldwide traffic of snowstorm in all years. Click on graph for more.
snowstorm
snow storm
blizzard