Thats just not so in scripture. In both testaments, Satan is referred to as a serpent. But snakes arent the only type of serpent. In the OT a serpent was identified by the hissing sounds it made. But other creatures also hiss. Like the gila monster, komodo dragon etc.
And Satan is ALSO referred to in both testaments as a dragon. We know before he caused Adam to betray God that he had limbs. As part of his curse God took away his limbs and made him crawl upon his belly as a snake - same Hebrew word.
So before the fall, Satan was a dragon, and after the fall, a snake. The same Hebrew word describes both creatures -- nachash.
Gen 3:1 Now the serpent was more subtil than any beast of the field which the LORD God had made. And he said unto the woman, Yea, hath God said, Ye shall not eat of every tree of the garden?
Rev 12:9 And the great dragon was cast out, that old serpent, called the Devil, and Satan, which deceiveth the whole world: he was cast out into the earth, and his angels were cast out with him.
Here the Greek word for serpent is ophis