When he came to Dumbledore asking for a job at Hogwarts, he hid Ravenclaw's diadem in the Room of Requirements. When Harry saw the memory, he noticed that although he did not look like the handsome Tom Riddle, his features were not snake-like as of then. Ravenclaw's diadem was his last Horcrux before Nagini (or Harry). If he didn't make any more Horcruxes until 1981, did he still look like he did on the day he asked for the job when he killed the Potters?
He looked like he did when he was ‘reborn’.
Though the Dark Lord isn’t explicitly described on the night he kills the Potters his appearance is unusual enough to scare a Muggle child, and further, from Harry’s nightmares of that night that it was the same as when he was returned to a body.
“Nice costume, Mister!’
He saw the small boy’s smile falter as he ran near enough to see beneath the hood of the cloak, saw the fear cloud his painted face: then the child turned and ran away … beneath the robe he fingered the handle of his wand … one simple movement and the child would never reach his mother … but unnecessary, quite unnecessary …”
- Harry Potter and the Deathly Hallows, Chapter 17 (Bathilda’s Secret)
We know that when he was returned to a body, the Dark Lord looked the same as when he killed the Potters, since Harry describes staring back at the face that haunted his nightmares - he’s almost certainly referring ti the nightmares he’d been having about the night his parents were killed by the Dark Lord.
“The thin man stepped out of the cauldron, staring at Harry … and Harry stared back into the face that had haunted his nightmares for three years.”
- Harry Potter and the Goblet of Fire, Chapter 32 (Flesh, Blood and Bone)
The Dark Lord’s appearance is described in more detail when he returns to a body, and from this description we learn both what he looked like when he killed the Potters and after his return to a body, since he looked the same.
“Voldemort looked away from Harry, and began examining his own body. His hands were like large, pale spiders; his long white fingers caressed his own chest, his arms, his face; the red eyes, whose pupils were slits, like a cat’s, gleamed still more brightly through the darkness. He held up his hands, and flexed the fingers, his expression rapt and exultant.”
- Harry Potter and the Goblet of Fire, Chapter 33 (The Death Eaters)
As for why the Dark Lord’s appearance changed between his meeting with Dumbledore, it’s possible the change in appearance caused by creating Horcruxes also has a gradual effect - the changes may not all happen right after the creation of each additional Horcrux. They may have continued over the years as well.
“I, who have gone further than anybody along the path that leads to immortality.” That was what you told me he said. “Further than anybody.” And I thought I knew what that meant, though the Death Eaters did not. He was referring to his Horcruxes, Horcruxes in the plural, Harry, which I do not believe any other wizard has ever had. Yet it fitted: Lord Voldemort had seemed to grow less human with the passing years, and the transformation he had undergone seemed to me to be only explicable if his soul was mutilated beyond the realms of what we might call usual evil …”
- Harry Potter and the Half-Blood Prince, Chapter 23 (Horcruxes)
Dumbledore never says exactly how or when creating Horcruxes transforms someone, so he didn’t necessarily mean that it happens all at once after creating additional Horcruxes. Therefore, it’s possible the Dark Lord’s appearance continued to change over the years without him making more Horcruxes.