There are a few ideas that are attributed to Ueshiba as regards hakama, some are probably true, some others are possibly apocryphal.... There is a popular thought that he wanted everyone to wear it as he considered it the proper wear of the samurai, and was very much of the idea that he was preserving samurai culture and ideals (whether or not he was is another question...). A part of that is the idea that each of the seven pleats were symbolic of the seven virtues of Bushido, for example. As far as that being more part of his other training, though, it's possible that it came from Takeda, although I wouldn't say that means that it's actually an old tradition either. I don't think Daito Ryu predates Takeda, though.
But, as with all things in this area, it's very much up to the individual system itself. Different systems, even those that wear hakama, will tie them in different ways, or some will wear an uwa-obi on the outside, others will only use kaku obi underneath the hakama, sometimes colour will be specified, other times it's very much personal choice, length can be different from one system to another, and more. But, again, the majority of systems tend to only wear them for Embu (demonstrations)... but, as that's how most people see these arts, it gets assumed that they're worn all the time, and that it's traditional. It's really not. Unless, of course, it is for that system.
And, just cause this has been bugging me, the "training in a suit" metaphor above isn't really accurate... it's better to think of it like doing army training in your Class-A Dress Uniform.... that only gets pulled our for public or official use.
