If you are 'snowed under', you have too much to do and not enough time to do it.
I'm sorry, I can't write that report for you right now – I'm snowed under with work today.
Mum didn't have time to bake a cake; she was snowed under with cooking the dinner.
I'm going to treat myself to a spa weekend. I've been so snowed under this week; I need some time to relax.
Don't confuse it with
When the snow falls so heavily that you can't leave the house, we say that you are 'snowed in'.
Wendy rang to say that she can't come for dinner tonight – she's snowed in!
A huge storm brought large amounts of snow to the Stockholm area of Sweden this week. Around 30cm of snow fell in one night, causing widespread transport disruption. A further 20cm of snow is predicted to fall in the coming days.