24/7 turnout is typically awesome for horses like the one you describe. My “husband horse” is a little QH mare who stocks up significantly behind and gets quite stiff if she must be stalled, but 24/7 turnout keeps her limber and happy for her job as a hunt horse. I also know several other horses who were not just stiff but really quite lame in their previous homes that have become sound and after proper conditioning are working very hard as hunt or trail horses on very rugged terrain - much harder work than at their previous homes - after they switched owners and were able to be kept all or mostly turned out.
Even if you can’t switch to 24/7 turnout in the winter is there any way you could increase the hours? In my experience, 24/7 turnout or close to it is even more beneficial in the winter as most people ride less, go for shorter rides, spend more time in the indoor arena and less out on the trail, etc. If that isn’t an option, as much gentle movement (walking) as possible in other ways such as lunging, hand walking, ponying, an additional walking ride per day, etc. will be helpful. When my QH mare had to be on stall rest for 6 weeks or so last year to prevent her tearing around the paddock or pasture while an injury healed, ~20 min hand walks or ponying twice a day wasn’t enough to prevent all the stocking up, but it did significantly reduce her stiffness. It really did seem like two walks spread out throughout the day were more beneficial to her than one long walk.
Some of my riding friends do keep their horses stalled (no turnout except the occasional run around the indoor arena while the stall is cleaned) and a few of them swear by Back On Track or other ceramic infused type blankets, boots, or wraps. A few feel that blanketing the horse very warmly during cold prevents stiffness as well. A couple of them feed joint supplements during the winter months. I don’t really see those horses often enough to have a good idea if any of those strategies are effective or not.