Answer
Wa `alaykum as-salamu wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Thank you dear brother for your question that shows your interest to know the rulings of Islam and to well perceive the misconceptions that may arise from some Shari`ah texts.
It is common in the texts of the Shari`ah, i.e. the Qur’an and the Sunnah that there are confusing texts; verses or hadiths. However, this confusion is an only outward one.
As for the hadith mentioned in your question, the confusion mainly arises from the word “men” that means –in Arabic – either “men in general” or “husbands”. In this hadith it means “husbands”.
Answering your question, Dr. Wael Shehab, PhD in Islamic Studies from Al-Azhar University and currently the Imam of the Downtown Toronto Masjid in Canada, states:
The hadith you referred to in your question is not reported by Imam Muslim. It is, rather, reported by Al-Bukhari. The hadith reads, “Men and women used to do ablution (wudu’) together during the time of the Prophet (peace and blessings be upon him).”
The meaning of this hadith is that in the Prophet’s lifetime husbands used do wudu’ (ablution) along with their wives from the same vessel or pot. There are other similar hadiths which indicate that the Prophet (peace and blessings be upon him) himself used to do ghusl (washing) and so his wives did from a single vessel or pot.
Imam Al-Bukhari mentioned the above-mentioned hadith under the title “Husbands and Wives Doing Ablution Together” which supports the fact that the hadith refers to husbands who used to do ablution from the same vessel where their wives did ablution too.
The hadith doesn’t, by any means, indicate that there was a public place for wudu’ where men and women used to do ablution together. Ibn `Umar, who reported the above hadith, didn’t say that he “saw” men and women doing ablution together, but rather he told that men (i.e., husbands) used to do ablution with women (i.e., their wives).
Moreover, it is historically known that there were NO basins in Madinah where people, men or women, might do ablution together.
Given the above, it is not acceptable for some people to use the above hadith to claim that women can bare their arms, feet and heads before men; their claim is in conflict with the Qur’anic verse that reads, “O Prophet, tell your wives and your daughters and the women of the believers to draw their cloaks close round them (when they go abroad). That will be better, so that they may be recognized and not annoyed. Allah is ever Forgiving, Merciful.” (Al-Ahzab 33:59)
Allah Almighty knows best.