Remember how in CoS, they talked about how Voldemort was so involved in the Dark Arts that he didn't look like himself anymore because of all the magical transformations he went through. It shows how obsessed he became with the Dark Arts and with splitting his soul so many times that even the way he looked changed. He's not even human anymore with all the Dark magic that it just makes sense that he would get more snake-like features - especially with being in Slytherin, speaking Parseltongue, having Nagini as a pet.. So by him just having slits and not an actual nose, it makes him more snake-like and at the same time, it makes him barely human.