Did Elsa's Mom Have Powers?

The implication, and it's only ever just that, is that Elsa and Anna's mother is herself somehow attuned to the magical forces such that Elsa was given the gift of superpowers. (Why Anna never received such powers is equally vaguely defined: just as Elsa and Anna's father had no powers, so too would she be power-free.

Did Elsa's mom have magic?

Elsa is shown a memory of her mother using air magic in the forest, and interacting with the elemental spirits. She is also shown a memory of Iduna saving King Agnarr, by calling out to the spirits with the same melody that Elsa has been chasing.

Did Queen Iduna have powers?

Despite her daughter Elsa having magic ice powers, Queen Iduna does not appear to wield any sort of magical abilities, making her a normal human being. Since she is a monarch, it is most likely that she is skilled in politics and diplomacy.