Was the serpent depicted in Genesis 3 just a snake, or was it Satan?

"Now the serpent was more crafty than any beast of the field which the Lord God had made.  And he said to the woman, ..."  Genesis 3:1 NASB

Eve did not appear to be surprised to hear the serpent speak and the serpent is described as "crafty", depicting purposeful intelligence and design.

How is this?  Did all animals originally speak, or just this one?

Strong's Concordance lists the word "crafty" as arum, described as "cunning (usually in a bad sense): - crafty, prudent, subtil."  In a fashion, the serpent is depicted as having the ability to distinguish right from wrong and to make informed choices.

Interesting.

I am aware that in traditional Christianity we ascribe the serpent's abilities as being due to possession by Satan, but I can't find biblical confirmation of that.

Most point to the depictions of the serpent in the book of Revelation, but I see that the word translated into English (according to Strong's) as "serpent" is "ophis",  "(through the idea of sharpnessof vision); a snake, figuratively (as a type of sly cunning) an artful malicious person, especially Satan: - serpent".

Not a reference to a snake at all, but rather to Satan's personality.  In other words, it appears that the characteristics of a snake are being given to Satan and not the reverse!

Why would God curse the serpent if it was acting solely under the influence of Satan?  Genesis 3:14-16

Thoughts?