Is it permissible for a woman to wear a wig inside the house only?

All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

It is not permissible for a woman to wear wigs because they come under the ruling about hair extensions. It is well known that applying hair extensions is one of the grave major sins. It was narrated that an Ansari girl was married, and she became sick, and all her hair fell out. Her family wanted to make her use hair extensions. They asked the Prophet, sallallaahu ‘alayhi wa sallam, about this matter and he said, "Allaah has cursed the woman who artificially lengthens (her or someone else's) hair and also the one who gets her hair lengthened." [Al-Bukhari and Muslim and the wording is of the former]

That Hadeeth blocks the means for using hair extensions under all cases, even though the purpose in itself is approved under the Sharee'ah, such as a woman adorning herself for her husband.

Allaah Knows best.