White Walkers are dismissed by nonbelievers as being in the same category as "Grumkins and Snarks"
Obviously, by season 7, we know that White Walkers are indeed real.
Is there anything in the books that would imply that Grumkins are real?
I have a pet theory that the faceless men are actually Grumkins in disguise.
There is no indication in the books as to what might they actually be.
We only hear about them from Tyrion's POV and he is a cynical man. He considers them characters from a fairy tale, nothing more than that. Qyburn also mentions them mockingly while referring to the Night's Watch. And as Skooba has established, From Sansa's POV as well who is supposed to be naive.
They can be dismissed as in-universe mythical creatures based on the information we have so far.
Tyrion mentions a list of such creatures:
"How kind of her." Tyrion made a waddling bow, but at the cabin door, he turned back. "What if we should find the queen and discover that this talk of dragons was just some sailor's drunken fancy? This wide world is full of such mad tales. Grumkins and snarks, ghosts and ghouls, mermaids, rock goblins, winged horses, winged pigs … winged lions."
ADWD - Tyrion III
It is rather unfair to compare the Others to them. Long Night did happen in-universe and there are many works dedicated to the whole affair. People however consider the Others to have passed into extinction and consider them like the mythical creatures now, while the Other mythical creatures never existed in the first place.
For known/attributed attributes/characteristics of Grumkins, see Skooba's answer on this very thread.
Grumkins are almost definitely not real, and it is even less likely they are Faceless men in disguise. We do not learn much about them, only mentioned in passing:
They are magical:
In Old Nan's stories the grumkins crafted magic things that could make a wish come true. - A Storm of Swords - Sansa V
They are implied to be short:
"Maybe he thought you were a grumkin." Tyrion glanced at him sharply. Then he laughed, a raw snort of amusement that came bursting out through his nose entirely without his permission. "Oh, gods," he said, choking on his laughter and shaking his head, "I suppose I do rather look like a grumkin. What does he do to snarks?" - A Game of Thrones - Tyrion II
Possibly steal/replace children
Once, when she was littler, Sansa had even asked Mother if perhaps there hadn't been some mistake. Perhaps the grumkins had stolen her real sister. But Mother had only laughed and said no, Arya was her daughter and Sansa's trueborn sister, blood of their blood. - A Game of Thrones - Sansa I
Nothing implies that they were ever real. Based on the descriptions we do see they might bear some shared traits with the Children of the Forrest, but the Children were known to exist (just extinct now) The comparison of White Walkers (Others) to the grumkins is that in the current time they might as well be the same.
