My mom's a hairdresser and owns her business. It's true about standing on their feet all day except this is a very old school method, new school stylists (esp posh ones) sit on stools to style your hair or some use these soft rubber rugs on the floor just for that so that they won't be hurting as bad at the end of the day. This will prolly depend on how/who you get trained by and who you end up working for.
My mom was very successful during her height (30's ~ 40's) and I think her family life suffered as a result. Just something to think about. Cuz like others pointed out, you'd prolly have to work weekends (usually you get way busier on weekends understandably). I grew up missing out on family outings on weekends unlike all my other friends. Even on her day off, if a customer called she wouldn't refuse to work.
There are also occupational hazards cuz you do deal with chemicals i.e. hair dyes, perm solutions (despite using gloves). Hair dressers are prone to certain ailments, I think I read studies that reported the chemicals affect your livers and certain other organs. Yeppers on carpol tunnel and things like wrist cysts and arthritis, too.
My mom had uterian cancer 5 years ago and she only took 2 weeks off for her operation and hospital stay! Business was back to normal after that. It is tough if you operate your own salon cuz just like Palermo said, you don't get paid if you don't work.