Ahem, 'open' hose or to use our reenactment vernacular, 'split hose' are for the 15thc just like closed hose in that they meet at the back and are quite near each other at the front, earlier, say 14thc and early 15thc can be more like th chausses. What you do see at WOTR is the early style, ie the hose coming to a point at the top, this is a much earlier (the odd excption ,see Catherine of Cleves Book of Hours), not only that but you seem pointed to belts, that is another thing altogether though.
hit the hip and meet at the back and front, for work, you can undo the back and have hanging, or rolled down.
Zauber is on the money basically.
I do wait for the old 'but I have mine for comfort', answer, hose are meant to be comfortable, if they are not then the following might be applicable:
badly made hose
improper use, eg tight hose being used done up whilst runnign around like a loon.
"What are you defining as 'underwear' Jenn? Strictly speaking this applies to the doublet as well surely? I find myself wondering about this. As a cook, I routinely work in shirt and hose. I refuse to get my doublet messy needlessly and I don't believe my C15 counterpart would have done so willingly either."
Depends, pants and shirt are typically the underwear, doublets are the foundation garment, taken later in time, a man in waistcoat was not undressed, nor was he partially dressed, but in shirts, unless in a decent context was considered undressed, tee shirts carry that over in some quarters. The Tres Riche heurres show men and women in their underwear whilst working in fields, I suspect that once on their way through town that they would at least put on their next layers, for decency's sake.
As for your doublet, well, you can use an apron mate or don't splash the food around so much