In Genesis, we find the serpent is described as the most cunning of all animals.
He is not described as the only one who can speak. Does this mean other primordial animals could also speak?
Haamek Davar explains that the snake did not and could not speak; rather, every creature has a mazal, an angel assigned to it, and it was the snake's mazal that spoke. [Presumably any mazal can speak.]
And I now see that Rav Saadya Gaon, quoted by ibn Ezra, says similarly. Others quoted there say Eve understood the animals' sounds. Ibn Ezra himself says the snake spoke, but other animals did not, and that's part of what's meant when Scripture says the snake was cleverer than the other animals (which, more generally, he says, means that the snake had sub-human-but-more-than-animal intelligence).