In American and Canadian English, plow is the preferred spelling of the farm implement and its related verbs. Plough is the preferred spelling in the main varieties of English from outside North America.
The spelling distinction applies to all senses of the word, including figurative ones. British and Australian writers always use plough, along with ploughed and ploughing; American and Canadian writers always use plow, plowed, and plowing. Both spellings are pronounced the same.
In winter he plows the streets, and in spring he trims the trees. [The Atlantic]
Russell confronted a man who had stolen a snow plow and was driving across the city. [Toronto Sun]
Plowing through a stack of mail, he came to an envelope that read “This is not a bill.” [Washington Post]
Outside North America
The larger ones had been removed by the boys, swinging pickaxes into the iron land before the ploughing began. [Independent]
It was me that opted to plough through the storm. [Sydney Morning Herald]
A man who ploughed into a crowd of revellers outside a bar in Rochdale has been jailed indefinitely. [BBC News]