The image of Asmodeus as a snake likely comes from some interpretations of his role in Jewish mythology. He is associated with lust, envy, and wrath, and some texts mention him tempting people with sensual pleasures, which could be interpreted as a snake-like temptation.
However, he is not inherently a snake-like creature. He is typically depicted as a powerful demon with wings and a terrifying visage, often holding a whip or other weapons.
It's important to note that interpretations of Asmodeus vary across different religions and cultures. His portrayal as a snake is not universal and likely stems from specific interpretations of his character and symbolism.