The Pantomime horse is a fake horse Pretending to be a real horse
Just like the Men pretending to be women & women pretending to be men.
Yours is an odd analogy.
Pantomime is a type of musical comedy stage production designed for family entertainment.
A pantomime horse is a horse costume used in theater which is not intended to be or look real. As you can see from the photo.
A transvestite is a person who dresses in clothes primarily associated with the other sex. They are parodies of whatever gender they are pretending to be. With these folks I get the comparison you make.
Transgender describes those who have a gender that’s different from the sex (male, female, or intersex) or binary gender (boy or girl) they were assigned at birth. This is more involved than simply wearing a costume - as does a pantomime.
Pantomime horse
Transvestite/drag queen Ru Paul dresses up in women's clothes... period.
Chaz Bono takes being transgender seriously.
Not only is Valentina Sampaio a serious transgender person, but she also successfully (IMO) pulls it off.
Valentina Sampaio is the first transgender Sports Illustrated model.