I totally agree about lots of movement and turnout, but I think the older creaky guys really appreciate being able to lie down in their own safe space at night sometimes.
I have a 27 yo who's lived out forever, but I'm building him a stall b/c he's started sleeping in the shed at night and I don't like to think of him being pushed around in there. He's not terribly stiff, but he's a big guy, and its a big deal for him to get up and down, and when he goes down to sleep he likes to stay like that for a while.
Totally depends on your horse. My 14 yo would knock me over to come in at night and he loves to lie down and sleep in his stall every night, but my 23 yo would hate it. There is certainly a difference in being cooped up in the stall all the time making you stiff, and just coming in on cold nights for a break, with lots of turnout in the day.
Just started my mare on Gluquestrian joint supp. a month ago for arthritis and ringbone. Big difference in the way she goes. I can ride her now and no limping at the trot. I highly recommend this joint supp. and lots of turn out. She is 23 going on 10 now.
Unless it is super duper nasty, I would leave him out. Give him lots of good hay, make sure he has warm water to drink, and if possible in his turnout shed, see if you cannot fashion something so he can have an extra wall to completely get out of the elements. Sort of like 3 1/2 sided shed.