Answer: As early as 1322, Rav Kalonymus ben Kalonymus (Even Bochan, p30) writes about the minhag to dress up on Purim: And on the fourteenth of Adar… one wears a woman’s dress, a necklace on his neck and acts like one of the fools…
The Mahari Mintz (17) writes that while cross-dressing is explicitly forbidden by the Torah (Devarim 22:5), as one wears such clothes on Purim to enhance one’s joy (as opposed to immoral purposes), it is allowed. He writes that he witnessed many such costumes and never saw the rabbanim object. The Rema (OC 696:8) quotes both strict and lenient opinions, and says that the minhag is to be lenient. Elsewhere (Darkei Moshe), the Rema writes that some even allow one to wear a costume made of shaatnez on Purim!
Nonetheless, the Mishna Berura (696:30) quotes several Halachic authorities (Taz, Bach, Shelah, etc.) who prohibit the practice. R’ Ovadia Yosef (Yechaveh Daas 5:50) writes that one should not even allow one’s children to cross-dress on Purim. Seemingly such costume was far more prevalent in the olden days as the Aruch Hashulchan (OC 696:12) writes that Jews no longer follow this practice.
While most contemporary poskim forbid cross-dressing, we don’t need to criticize those who do dress up in such a manner.