"During the 19th Century some collectors, especially Donald A. MacKenzie, deliberately rewrote Cailleach tales and gave them a mythological element by adding Brighid as goddess of spring. Yet none of the orally transmitted tales make this conection. Brighid, the goddess of Imbolc is quite independent from the Cailleach. The Cailleach as winter goddess stands alone."
The link between Brighid and the Cailleach is mentioned frequently in modern writings about Brigit in particular. For the whole article on the Cailleach see comments section of this post. (Comments section here includes some debate as well.) SEE ALSO Seren's post at her website Tairis:
"There’s no clear evidence of a Maiden/Mother/Crone goddess concept in Scottish folklore."