This is an English locational surname. It originates from any of the three villages known as East, North, and South Cowton near the county town of Northallerton, in the county of North Yorkshire. Curiously none of the villages have anythig to do with cattle, probably because the life in every village in ancient times revolved around rthe keeping of livestock.
In this case according to the Oxford Dictionary of English Place Names the meaning is the the farm of Cuda, the latter being a personal name of the pre 7th century which may have translated as "kiln".
Locational surnames were usually "from" names. That is to say names given to people after they left their original village to move elsewhere, often in search of work. The easiest way to identify these "strangers" was to call him or sometimes her, by the name of the place from whence they came.
Spelling being at best indifferent and local dilaects very thick, soon led to the development of "sounds like" spellings.
In this case early examples of the surname recording taken from suriving registers of Yorkshire include:
John Coweton at North Burton in the East Riding of Yorkshire on August 13th 1552,
and Agnes Cowton, who married Antonius Welles at Ripley, near Ripon,
on August 15th 1574.