Individual experiences may differ but when I had to sleep in body armor in Iraq, the next half a day sucked. Sure its doable, but there is a great difference between grabbing some shut eye, and getting real rest. After a few days of this you're more like a zombie than an active person, and why that first time you sleep in a real bed you fall into the "combat coma" lol.
I never wore any reenactment armor but I think it would fit this same style pretty close. Sure anyone can tough it out a day or two, after a few days or a week though thats going to really take its toll. Basic hygiene will always be an issue, weather plays an important role, and think of the life styles and training as well. Todays training for real soldiers is far superior to what was normally given, and the equipment we use is designed to improve the duration of wear. Layers of padding and leather leave little room for the body to breath especially when another layer of metal is added over it, hell even our casual shirts are made of better material than what they were made of back in the day.
I'm not sure what penalties I may apply to players who have to sleep in armor, but luckily my group tends to avoid this for realism unless, its just not safe enough. Limiting rests to short rests only while in armor sounds good to me though.