Are leggings trousers?

According to the Oxford Dictionaries, yes.

We define leggings as ‘tight-fitting stretch trousers, typically worn by women or girls’.

A key concept in a dictionary entry is the ‘genus term’ – the part of the definition which answers the question ‘what type of thing is it?’. The genus term is a broader category into which the word being defined fits, and can be used to place closely related words into groups, or semantic categories. Our entry for leggings, therefore, uses the genus term ‘trousers’, firmly placing them in that group alongside jeans, cords, and culottes. And they certainly seem to fit our definition of trousers: ‘an outer garment covering the body from the waist to the ankles, with a separate part for each leg’.

Some critics however, have an issue with leggings as an ‘outer garment’.... (more at the link)

Photo credit: American Eagle Outfitters.