My oldie is the same, stiff after standing in, not lame, probably a bit arthritic but not formally diagnosed. I was told last year by my vet to keep him moving as long as possible and if he needed Bute, then fine, it’s much better to do that than to stop riding. He was great up until March, when lockdown and a health problem put a stop to all riding. He deteriorated rapidly in just 4 months, looked 5 years older, much stiffer, loss of muscle, and he looked miserable.
I started gentle walking again a few weeks ago with him, and already he’s looking and feeling better, and I’ll have no qualms about giving him a bute if he needs it to carry on. We used to trot a little on the roads just to avoid traffic, and will be doing it again when he’s a bit fitter I dare say. Every horse is different, be guided by your vet, your horse and a bit of common sense and I’m sure you’ll make the right decision.