The Mishna in Masechet Mo'ed Katan records the provision enacted by the Sages forbidding washing clothes during Chol Ha'mo'ed. This prohibition was enacted out of concern that people might leave their laundry for Chol Ha'mo'ed and thus begin Yom Tov with soiled clothing. The prohibition against laundry on Chol Ha'mo'ed ensures that everybody will wash their clothes before Yom Tov.
The Mishna does, however, make a number of exceptions to this rule. Firstly, Halacha permits washing towels including bath towels, hand towels and dish towels during Chol Ha'mo'ed. Since towels are frequently used and thus washed regularly, the Sages allowed laundering towels during Chol Ha'mo'ed. However, the Magen Avraham (commentary to the Shulchan Aruch by Rabbi Avraham Gombiner, Poland, 1637-1683) writes that nowadays, when people do not ordinarily wash towels every day, it is forbidden to wash towels during Chol Ha'mo'ed. Chacham Ovadia Yosef cites this view in his work Chazon Ovadia (p. 198). It is, however, permissible to wash handkerchiefs during Chol Ha'mo'ed.
Pregnant women who wear special stockings for comfort should preferably purchase enough pairs before Yom Tov to last throughout the holiday. Nevertheless, if a woman did not purchase enough pairs of these garments before Chol Ha'mo'ed and needs to wash a pair during Chol Ha'mo'ed, she is permitted to do so.
It is likewise permissible to wash children's clothes on Chol Ha'mo'ed. If one washes by hand, he may wash only each garment individually as needed; he may not wash several garments simultaneously. Clothing of infants, however, which become soiled very frequently, may be washed even several at a time. If one uses a washing machine, then he may wash many children's garments simultaneously, even those of children who are no longer infants. Even in such a case, however, it is forbidden to add adults' clothing to the machine.
Finally, although one must ensure to wash enough undergarments to last throughout the festival, if one must wash undergarments for wearing on Chol Ha'mo'ed he is allowed to do so. Since today people change their undergarments each day, the prohibition against washing clothes during Chol Ha'mo'ed does not apply. Nevertheless, as mentioned, one should preferably ensure to prepare enough undergarments to last throughout the festival.
Summary: Generally speaking, it is forbidden to wash clothes during Chol Ha'mo'ed. Some views forbid washing towels, as well. It is permissible to wash handkerchiefs on Chol Ha'mo'ed, and to run a machine wash of children's clothing. One should ensure to purchase and wash enough undergarments to last for the entire holiday, but if one must, he may wash undergarments to wear on Chol Ha'mo'ed.
