It has become customary among the Jewish nation to refrain from taking haircuts during the Omer counting period: according to the Ashkenazi custom, until the 33rd day of the Omer and according to the Sephardic custom, until the morning of the 34th day of the Omer (as we have already explained regarding getting married during the Omer). Some Sephardic individuals act leniently with regards to haircuts in accordance with the Ashkenazi custom, i.e. taking haircuts beginning from the 33rd day of the Omer. Those who act leniently in this regard (even Sephardic individuals) have on whom to rely.
Those who are truly G-d-fearing customarily abstain from shaving their beard during the Omer period as well. However, there are those who rule leniently for individuals who are truly distressed as a result of not shaving their beard, for the Radbaz writes regarding such matters which are not actual obligations as a result of an edict of our Sages and is merely a custom, in a case of such distress, there is room for leniency. Nevertheless, it is indeed correct and proper to follow this custom which was observed by our ancestors for many generations with regards to refraining from shaving one’s beard during the Omer period (it is especially worthy to be stringent until Rosh Chodesh Iyar).
Women are not included in the prohibition of taking haircuts during the days of the Omer, for even with regards to actual mourning for a relative who has passed away (for which a male mourner must abstain from taking a haircut for the entire thirty-day mourning period), Maran HaShulchan Aruch rules that women are not included in this prohibition and are permitted to take haircuts during the thirty-day mourning period. If so, this would certainly apply to the mourning customs observed during the Omer period in that a woman need not abstain from taking a haircut. The same would apply to the three week period between the Seventeenth of Tammuz and the Ninth of Av that the prohibition to take haircuts applies to men alone, but women are permitted to take haircuts.