Definition: having too much to do
Example: Steve would have loved to attend the all night screening of Sex and the City episodes with his wife, but unfortunately he was snowed under at work and wouldn’t be home in time. Poor Steve.
There doesn’t seem to be any fancy origin for snowed under. It simply describes the feeling of being smothered or crushed by the weight of work. Just like you would under a heavy snowfall. That’s it.
In a little sidebar about snow related terms, the word ‘blizzard’ was around for many years before it had anything to do with snow. It originally meant a sharp blow or a gunshot. No snow in sight. It wasn’t until 1870, when an Ohio newspaper described a particularly bad snowstorm as a ‘blizzard’, that the word took a right hand turn into a different meaning.