Assalamu alaikom,
I am going to visit my mother this month. I live in Egypt and she in the states. My husbands father will travel with me just to drop me off with my mother and then he will leave. Anyhow, she has suggested that we do activities like ride bicycles, horses and go for walks or running together. Of course it will be in public..
I am fully covered and I also wear jeans under my abaya, so no chance of anything coming uncovered... I have read many fatwas and some say it is okay to do these activities and some say it is not. The main reason some say it is forbidden is because the wind from riding the bicycle may blow and cause her clothes to form her shape. BUT if that is the case then wouldn't it be forbidden to go outside in public with their husbands on a windy day?
Oh and the running and riding horses.. My husband thinks it may be forbidden to do this in public because a womans breast or buttocks might bounce up and down and cause men to look at her. But I think he is wrong because the women in the days of the prophet (saw) rode camels and horses and Aishah (ra) and the prophet (saw) had a running race.
Please help me. I don't want to do anything wrong. If it is forbidden I want to avoid it.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

In principle, it is permissible for the woman to practice the sports of cycling, horse-riding or running if the Sharee‘ah criteria are met. Doing these activities before non-Mahram men most likely leads to violation of Sharee‘ah rulings, as previously clarified in Fatwa 87602. We do not know how you understood that what you mention is the main reason for preventing women from riding bicycles. In fact, there is no analogy between the two cases. That is because when the woman rides a bicycle, she makes some movements and actions which may cause her to fall into religious prohibition.

In fact, your husband was right when he told you that a woman is not allowed to do these sports in front of non-Mahram men due to the evil consequences we mentioned above. Moreover, the race that was between the Prophet, sallallaahu ‘alayhi wa sallam, and his wife ‘Aa’ishah did not take place in the presence of the Companions. ‘Aa’ishah said: "When I was young, before I put on weight, I went out on a journey with the Prophet, sallallaahu ‘alayhi wa sallam. He ordered his Companions to proceed ahead of us, and after they did he told me to race with him. I won the race." [Ahmad]

Therefore, if you can do these activities in sport halls for women or in places exclusive to women or in a place where only your husband and Mahram relatives can see you, go ahead and practice these activities. Otherwise, you should apologize to your mother in a kind and gentle manner.

Allaah Knows best.