While it is not explicitly stated in the books, it is believed that Voldemort must have lost his nose after he started using Nagini's venom to keep himself alive. Nagini was a woman but a Maledictus with a blood curse that made her eventually become a snake forever. It is possible that her venom too was affected by this curse and therefore when Voldemort used this venom extensively, it transformed him into his strange appearance with snakelike traits including the lack of a nose, red eyes and pale skin. It may also have something to do with him ripping his soul apart several times to make Horcruxes and that the last Horcrux he made happened to be Nagini herself.