There is a famous Zen Koan that goes, as follows;
A monk asked Joshu, “Does a dog have the Buddha nature?” Joshu retorted, “Mu!”
There's been quite a lot of speculation as to what,exactly, it's supposed to mean. I'm not going to attempt an answer to that.....but type in the words "MU Koan"
(without the quotation marks) into Google and you'll see enough examples to keep you busy for awhile.
As if to show that a dog does not have Buddha nature, we find a story of a dog who lives in a Buddhist temple in Okinawa who has taken to imitating the prayer posture in order to get treats from temple visitors.