Melachah on Rosh Chodesh
According to halachah, it is permissible to do work on Rosh Chodesh. However, women have the custom of refraining from work on Rosh Chodesh—and this custom is binding—as a reward they received for refusing to give their jewelry to make the Eigel, the Golden Calf, and for not having worshipped it. The three yomim tovim of Pesach, Shavuos, and Sukos correspond to Avrohom, Yitzchok, and Yaakov respectively, whereas the twelve days of Rosh Chodesh every year correspond to the twelve tribes (Tur Orach Chaim 413). After the men sinned with the Eigel, the twelve days of Rosh Chodesh were taken from them as a non-work holiday and given to the women. In addition, Rosh Chodesh is associated specifically with women because every month a woman renews herself after her immersion in the mikvah and becomes closer to her husband, which is considered a yom tov for her.
What type of work should women not do on Rosh Chodesh? The essential idea is that a woman should not treat this day as a regular weekday and do all of her usual household chores, but should refrain from some level of work, depending on the custom in her particular community. In many sefarim, the custom of refraining from weaving and spinning is mentioned. Some poskim say women should not sew, and others say women should not do laundry, even using a modern-day washing machine. Getting and giving a haircut and cutting nails on Rosh Chodesh are technically permissible. However, in his tzava’ah, will, Rabbi Yehuda HaChossid wrote that due to a concern of danger, one should not get a haircut or cut their nails on Rosh Chodesh.