Wiktionary
vb. (context idiomatic English) To have a lot of things to do, usually work-related.
Usage examples of "be snowed under".
Snow is falling for reasons of de-Nazification: everybody is putting objects and facts out into the severe wintry countryside to be snowed under.
I did not expect to be snowed under with notables on a simple visit to a museum.
There'll be just a trickle of eggs at first, but once they get cracking we'll be snowed under.
I think he warned you that we were about to be snowed under by a huge work load and suggested you take off and leave the rest of us more expendable Jumpers to struggle under the pile.
He was glad he was not the chief engineer: Murdock would still be snowed under with paperwork.
I'm not handing out compliments now - I've moved on to the brickbat stage, and believe me there are some people out there who deserve to be snowed under with barrels of dreck for abdicating their responsibilities as thinking individuals.