A controversial topic that is raised is, Can wear women trousers? The answer is yes.
But let use deal with a few things with respect to Deuteronomy 22:5 that must be clarified and out of the way:
"Deuteronomy 22:5 “A woman shall not wear a man's garment, nor shall a man put on a woman's cloak, for whoever does these things is an abomination to the Lord your God."
Some translations go however mention another aspect that most seem to overlook and it can be found in other translations, I'll give one but the rest you can read yourself:
"English Revised Version
A woman shall not wear that which pertaineth unto a man, neither shall a man put on a woman's garment: for whosoever doeth these things is an abomination unto the LORD thy God." http://biblehub.com/deuteronomy/22-5.htm
The phrase used in the passage in Hebrew is kĕliy geber. While keliy can be used of garments and clothes, it is also a reference to utensils or equipment. In other words, it is not just a prohibition of wearing clothes of the opposite sex, but is also a reference saying that women shall not use or wear the utensils specifically assigned to a man, which would also entail military garb.
There is one particular article I recommend looking at for more information: https://reformedtheonomy.wordpress.com/2016/02/09/women-in-the-military-and-in-combat/
Before anyone tries to argue women are used in the military by Israel, Here is another article I direct you to: http://warfighternews.com/2014/03/21/debunking-the-israeli-women-in-combat-myth/
Am i arguing Christians are under the Old Testament law? No. we should be asking, which laws are for Christians today and which are not?
The principle in the passage that applies to us today is recognizing the distinction between men and women and their roles in family life, not just in clothes, but behavior too. This is not to say that women are not equal to men in terms of dignity in the of the eyes of God, to say men and women are not equal in terms of dignity in the eyes of God would be a lie.
It does not matter if you are a man or a woman, living a holy life in God's sight is what counts and BOTH genders need salvation.
Transvestism is a sin, It robs people of their distinction and even in today's world, people are trying obliterate that distinction.
I won't go into detail here as to whether or not a woman can work, What I will say is this, There are jobs women have that men cannot and there are jobs men have that women cannot. There are jobs applicable for both genders and there are jobs for specific genders, either male or female. The principle ultimately in Deuteronomy 22:5 calls for men and women to recognize their roles and not seek to violate and destroy the barrier.
Now, with that out of the way, Let's get to the question, Can women wear trousers. Yes, However....
While I believe women can wear trousers, they must be trousers that show they are a woman and likewise, the man must wear trousers that make show they are a man. I don't suggest that women or men should dress in a kinky manner, as we both must dress modestly and not have our attire cause others to lust over us.
Truth be told, I take issue with men wearing really skinny jeans. When I say that, I am not talking about a mountain of a man like Arnold Schwarzenegger who had a huge structure before his acting career and thus a baggy pair would be quite skinny, I am talking about the little guys, including myself. In our case, wearing really skin tight jeans would be inappropriate if it makes us feminine. Women can wear jeans or trousers, but they must be feminine, I seriously would not recommend a woman to wear casual baggy trousers but certainly thin jeans that distinguish them from the men would be allowed.
While there are many men out there who are well intentioned in not allowing women to wear trousers, I feel this legalistic. As long as there is a distinction between women's clothing and men's clothing, then trousers are acceptable. It's like the Japanese Kimono or Middle Eastern Robes, there are distinctions between the clothes of both sexes, You can't shove a male into female kimonos and vice versa. Ancient Israelites wore robes, but the robes clearly had a distinction between male robes and female robes, Men had to wear men's robes and Women had to wear women's robes. Trousers have the same principle, Men have to wear men's trousers and Women have to wear women's trousers. The basic principle is that the clothes do NOT cause gender distinction to be lost and before you ask, no a man cannot wear a dress.
I leave you to judge my words.
PS, there might be baggy jeans for Arnie, but you get the idea.