TL;DR: We have the case of the Night's Queen who is spoken about in the books and appears in one of the Histories & Lore videos in the show. Whilst she is spoken about as an Other/White Walker she could actually be a wight as it is never stated explicitly although I'd say the evidence points to her as being an Other/White Walker.
We also have evidence of some potential hybrid Other/human species in the books and in the show it is implied that Craster sacrificed some of his daughter wives as well as the sons.
Game of Thrones
There is mention of the “Night’s Queen” in the series though it is actually from one of the Histories & Lore videos, as far as I’m aware nothing is mentioned in the main episodes.
We Free Folk have our stories, too. About how one of your king crows found something cold in the woods... with bright blue eyes. How he brought her home, through your wall, and declared himself "Night's King". For thirteen years he and his queen ruled over his brothers, making sacrifices as black as their cloaks. Lucky for you southerners, the Free Folk rallied to a King-Beyond-the-Wall, as we will when need be, and marched on the ancient castle he had taken as his own, the Nightfort. With the help of the Starks, we killed the demon and cleansed your precious watch. An' then they thanked us, an' kicked us back across the wall... as you always have.
Game of Thrones, Histories & Lore, "The Night's Watch" - Ygritte
From this all we know of her is that:
- she was “cold”
- she had bright blue eyes
- she was the Night’s King’s queen
- she was killed by the Free Folk and Starks
From this we know she got her title from being the Night’s King’s queen though there is no evidence that she actually had that title. From the description of her it could be said she was a White Walker but we don’t know for sure.
Here are some screenshots from the Histories & Lore video:
The Night's King finds the "Night's Queen".
"The Night's Queen" rides back to the Wall.
"The Night's Queen" is made queen.
"The Night's Queen" is killed.
We also have a hint that in the show some of Craster's daughter wives contracted greyscale and that he took them out into the woods. It is heavily implied here that he is using them as sacrifices to the White Walkers like he does with his baby sons. As such there could be some female White Walkers from this.
GILLY: What do you call it in the South, what happened to your face?
SHIREEN: Greyscale. What do you call it north of the Wall?
GILLY: I don't know. But two of my sisters had it. They both died. How did they cure you?
SHIREEN: I don't remember. I was a baby. Lots of people came and tried, I think. Whatever they did, it went away. What happened to your sisters?
GILLY: My father made them move out of the keep into the huts outside. None of us were allowed to go near them. But we heard them. Especially at night. They started to sound... not like themselves.
SAM: Did you ever see them?
GILLY: Only once at the end. They were covered with it. Their faces, their arms. They acted like animals. My father had to drag them out to the woods on a rope.
SHIREEN: What did he do to them in the woods?
Gilly is afraid to answer. Selyse enters the room before she can.
Game of Thrones, Season 5 Episode 2, "The House of Black and White"
A Song of Ice and Fire
In the books we have mention of the Night's Queen who was the downfall of the Night's King as the ruled at the Nightfort. It is only heavily implied that she was an Other but from the context of the story she probably was.
As the sun began to set the shadows of the towers lengthened and the wind blew harder, sending gusts of dry dead leaves rattling through the yards. The gathering gloom put Bran in mind of another of Old Nan's stories, the tale of Night's King. He had been the thirteenth man to lead the Night's Watch, she said; a warrior who knew no fear. "And that was the fault in him," she would add, "for all men must know fear." A woman was his downfall; a woman glimpsed from atop the Wall, with skin as white as the moon and eyes like blue stars. Fearing nothing, he chased her and caught her and loved her, though her skin was cold as ice, and when he gave his seed to her he gave his soul as well.
He brought her back to the Nightfort and proclaimed her a queen and himself her king, and with strange sorceries he bound his Sworn Brothers to his will. For thirteen years they had ruled, Night's King and his corpse queen, till finally the Stark of Winterfell and Joramun of the wildlings had joined to free the Watch from bondage. After his fall, when it was found he had been sacrificing to the Others, all records of Night's King had been destroyed, his very name forbidden.
A Storm of Swords, Bran IV
That maesters themselves don't believe she was a "corpse queen" but probably someone from the Barrowlands which lends evidence to the fact that she may not have been an Other. Howevber, it's worth noting that the maesters seem to have pushed all of the supernatural away as folk stories and fairy tales and so their judgement in cases like this is clouded.
Yet over the thousands of years of its existence as the chief seat of the Watch, the Nightfort has accrued many legends of its own, some of which have been recounted in Archmaester Harmune's Watchers on the Wall. The oldest of these tales concern the legendary Night's King, the thirteenth Lord Commander of the Night's Watch, who was alleged to have bedded a sorceress pale as a corpse and declared himself a king. For thirteen years the Night's King and his "corpse queen" ruled together, before King of Winter, Brandon the Breaker, (in alliance, it is said, with the King-Beyond-the-Wall, Joramun) brought them down. Thereafter, he obliterated the Night's King's very name from memory.
In the Citadel, the archmaesters largely dismiss these tales—though some allow that there may have been a Lord Commander who attempted to carve out a kingdom for himself in the earliest days of the Watch. Some suggest that perhaps the corpse queen was a woman of the Barrowlands, a daughter of the Barrow King who was then a power in his own right, and oft associated with graves. The Night's King has been said to have been variously a Bolton, a Woodfoot, an Umber, a Flint, a Norrey, or even a Stark, depending on where the tale is told. Like all tales, it takes on the attributes that make it most appealing to those who tell it.
The World of Ice and Fire, The Wall and Beyond: The Night’s Watch
It is worth noting that Old Nan states that the wildling woman would lay with the Others and a hybrid species were created which could have been what the Night's Queen was.
The man had been taken outside a small holdfast in the hills. Robb thought he was a wildling, his sword sworn to Mance Rayder, the King-beyond-the-Wall. It made Bran's skin prickle to think of it. He remembered the hearth tales Old Nan told them. The wildlings were cruel men, she said, slavers and slayers and thieves. They consorted with giants and ghouls, stole girl children in the dead of night, and drank blood from polished horns. And their women lay with the Others in the Long Night to sire terrible half-human children.
A Game of Thrones, Bran I