In John Gill's commentary on Gen. 3:1, he says,
the words therefore may be rendered, "that serpent"; that particular
serpent, of which so much is spoken of afterwards; "or the serpent was
become" F20, or "made more subtle", that is, not naturally, but
through Satan being in it, and using it in a very subtle manner, to
answer his purposes, and gain his point:
Herein lies the discussion: Is it a Literal 'serpent'(snake), that can stand up or have 'feet'? Not only that, but can it be more subtle(clever) than Adam and Eve, engage in a dialogue and be 'cursed' for it; along with being told it's 'seed' would be crushed by the woman's 'seed'?
That the serpent represents Satan is certainly biblical; in Rom. 16:20 Paul says,
And the God of peace shall bruise Satan under your feet shortly. The
grace of our Lord Jesus Christ be with you. Amen.
In Rev. 20:2 it says,
And he laid hold on the dragon, that old serpent, which is the Devil,
and Satan, and bound him a thousand years.
It becomes clear then, that Scripture interprets the 'serpent' as Satan.
But what about the 'serpent/snake'? Can Satan 'inhabit' snakes and suddenly give them speech and intellect?
St. John Chrysostom, in his homily on "The Snake's Question", says
The author of evil, accordingly, seeing an angel who happened to live
on earth, was consumed by envy, since he himself had once enjoyed a
place among the powers above but had been cast down from that pinnacle
on account of his depravity of will and excess of wickedness. So he
employed considerable skill so as to pluck the human being from God's
favor, render him ungrateful and divest him of all those goods
provided for him through God's loving kindness. What did he do? He
discovered this wild animal, namely, the serpent, over coming the
other animals by his cunning, as blessed Moses also testified in the
words, "The serpent was the wiliest of all the beasts on the earth
(127a) made by the Lord God." He made use of this creature like some
instrument and through it inveigled that naive and weaker vessel,
namely, woman, into
his deception by means of conversation. "The serpent spoke to the
woman," the text says.(taken from here)
While it is certainly true that Satan can inhabit animals(the herd of swine-Matt. 8:32), or that animals could talk-witness Balaam's donkey, although the Lord, not Satan, opened the mouth of the ass,(Num. 22:28)
28 And the LORD opened the mouth of the ass, and she said unto Balaam,
What have I done unto thee, that thou hast smitten me these three
It becomes problematic when a "beast" becomes a specific object of judgment by God for doing what it was created to do by God in the 1st place. Since a reptile does "not chew the cud", it would be an unclean animal, whether it crept along the ground or not. Therefore, the question of whether or not it 'fell' on the order of beasts is moot.
What one must consider is the bible is not a book of 'science', it is a book of truth.
The 'truth' of what was recorded in Gen. 3 is that God judged Satan, rightly called a "serpent", since his actions were 'serpentine' and spells out his destruction, as well as the 'animal' he masqueraded in. The fact that snakes slither on the ground is not the issue; the fact that the 'serpent' beguiled the woman through a lie is, and one which must be taken notice of.
Finally, the purpose of this passage is to outline the entire history of man, and the conflict between good and evil. Both Jesus(the woman's seed), and the Antichrist(the serpent's seed) are introduced, and the conflict between them; with the woman's seed ultimately crushing the head of the serpent.