You can ask Josie if she'll get you a long bath after you've just found Skyhold. As it is, lots of civilisations have different etiquette when it comes to bathing, cleanliness. The Vikings, for instance, we're all about looking after themselves, especially before battle. They washed almost everyday, especially on a Saturday, spent time on their hair and grooming, regularly cleaned and changed their clothes etc. It was also recorded that they washed their hands before eating and had oral hygiene which exceeds many even today. In the middle east, especially with Muslims, bathing in running water and cleaning oneself is both a religious and personal routine which is strictly kept to.
Going from in game, I don't think personal hygiene follows the same route of European Middle Ages. Bathing is mentioned often (mainly around Blackwall, even Cole gets in on him not brushing his hair.) and you come across the odd large copper bathtub where you go. I imagine that out and about, our characters would take time to wash off blood etc in nearby streams and will probably give themselves a once over before they settle down for the night, even if it's with cold water.
Actually, I'd say that our western culture has an almost unhealthy obsession with bathing and cleaning. I know people who work light office jobs and shower twice a day. And if you think BO is bad, having to sit next to someone on the bus who has literally doused themselves in perfume and cologne is almost worse. Things like shampoo and conditioner only really came around in the early 20th century, mainly because hair naturally regulates it's oil production and so "greasy" hair was rare and usually linked to a medical condition. Our hair tends to produce more oil now because we strip down our scalp with detergents and then put "other" oils back onto it via conditioner.
Anyway, enough ranting from me. The subject of personal hygiene over the ages is a very interesting one.