When Voldemort killed the Potters, he still had his original body, that of Tom Riddle, and though his looks would have been distorted then because of the creation of his Horcruxes, he would still have had a nose at that time and would not be as snake-like. He lost his original body when he tried to kill Harry and the curse rebounded on him.
The body he has now, with the snake-like features, and as everone is so focused onn, lack of nose, was created later through a potion and looks the way it does because it was magically synthesized. It is likely as snake-like as it is because Voldemort fed on snake venom, and largely incorporated his snake in the task of building himself a new body.
Actually, I don't think Voldemort did lose his nose. According to the series, I think he had two slits for a nose. I could be wrong about that. But even so, his entire face changed when his body was reformed through Flesh, Blood, and Bone