The topic of women wearing sheitels is controversial and we see totally opposing rulings from two of the greatest poskim of our time:
Rabbi Moshe Feinstein presents the Ashkenasic view in Igrot Moshe, Even HaEzer II:12: “Although some sages forbid the use of wigs, most allow it, including our chief halachic authorities…You cannot halachically prevent your esteemed rebbetzin from wearing a wig. Even if you wish to be strict, you may not force your own strictures upon her, for this is exclusively her realm.”
Rav Ovadiah Yosef represents the Sephardic community and has a much stricter approach in Yabia Omer V, Even HaEzer 5: “We need not be so impressed by wives of chassidic leaders wearing wigs for it runs counter to the Sages’ will. The law clearly follows the majority of Achronim who forbid the use of wigs and it is a great mitzvah to publicize the prohibition before the masses. This refers particularly to those Sephardic women who from time immemorial have treated it as forbidden and only now have begun to learn from those women who treat the Sages’ will lightly.”
How does this shake out in practice? Many women in the United States follow Rav Moshe’s ruling and wear wigs. Sheitels are often necessary for work purposes outside of Israel where it would not be professional to wear a hat or a scarf. In Israel, there is no need to wear a sheitel for professional reasons. Most Sephardic and religious Zionist women wear hats or scarves, even to work. In Charedi circles both in Israel and abroad, sheitels are mostly the hair covering of choice.