It seems to have been listed in the 1913 version of Webster from "Cowper." Maybe this is a good etymology question for Michael Quinion of World Wide Words.

Interesting. However, the word (dray) must be archaic now for all practical purposes. I read a recent publication on rodents in my local library and in the chapter on the Eastern Gray squirrel (Sciurus Carolinensis), the author refers to their habitats as "nests". Eastern Gray squirrels were brought to California during the Second World War along with the possum for the benefit of Southern soldiers in the U.S. military to hunt. By the late 1970's, they arrived in Washington State and are now quite abundant in the Seattle area.

I too thought it must be archaic, but then why all the Google images? People don't usually label pictures of things with archaic words.

It's not at all archaic - I've known the word for years, and I'd certainly use it should squirrels' nests come up in conversation. OK, realistically I don't move in any circles in which squirrels are discussed with any frequency, and I have no real evidence as to whether those who do would find "dray" current or archaic. But I think I've heard it a couple of times on wildlife programmes, and I imagine that anyone who has much to do with squirrels would at least be passively aware of the term, whether or not they'd actually use it themselves.

Tim's correct. Drey with an "e" is still the proper word for a tree squirrel's leaf nest, in use by squirrel biologists (I know three of 'em) if no one else. Thinking the word needed a little broader currency, I used it in the title of a back in March.

...the title of a blog post, I meant to type.

I knew I was getting on in years but, I would never describe myself as 'archaic'! And yes here in England 'dray' is used quite commonly as the description of a squirrels' nest.