It's because GRAY is a West Saxon word for the quality of light, while GREY is an Anglian word for everyday objects. And everyday objects are typically earthy, warmer, or more neutral.
To explain: West Saxon and Anglian are both dialects of Old English. West Saxon was the politically dominant dialect, but Anglian was the more popular spoken dialect. So a lot of Old English texts are written in West Saxon, but what we know as Middle English and Modern English descended more from Anglian because it was spoken by more people.
So grey (the Anglian word) shows up when authors are describing everyday stuff. Like in this sentence describing a grey beard from Holy Boke Gratia Dei: "The hed of Petir is a brood face with mech her on his berd and that is of grey colour be twix whit and blak."
Any Middle English text you read, you'll find Anglian grey is the word the author prefers to describe everyday things. Grey wool, grey feathers, grey stones, grey horses.
By contrast, gray (the West Saxon word) shows up when authors are describing the qualities of light.
A gleaming gray sword, a deep gray lake, a misty gray morning, cold gray marble, sad gray eyes. Like in this sentence from The Siege of Jerusalem: "They glowes of graie steel that were with gold hemmyd." More often than not, gray describes an impermanent or glimmering quality of light.
There's even an instance where a Middle English author uses both, and you can see how one spelling is more about the quality of light while the other is more about the color of the animal: "The cerkyl or the roundel off the eye ys sumtyme graye lyke the ey off a catte, sumtyme blak grey lyke the eyn off doggys."
("The circle or round of the eye is sometimes gray like the eye of a cat, sometimes black-grey like the eyes of dogs.")
The reason Americans use gray and not grey is because Noah Webster hated the English. :)
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