It *may* be an idea to fork out on some good arthritis treatments now while it is mild as some will actually make a good job of reversing the effects --- I've witnessed the good effects of cartrofen in dogs although I'm yet to see it's effectiveness in horses - it has had good reviews though. Very expensive unfortunately - if it is mild cod liver oil is prob. A better option although it is of pretty limited effectiveness.
Swelling --- how long is he kept in the box for? - does he have time in a field? Lack of exercise is often a large contributor to swelling. When one (any species) isn't exercising the heart rate and strength of beat decreases which means that often there isn't enough pressure (particularly in the older horse) for blood to make a proper circulation - this leads to a build-up of fluid in the extremities which causes swelling. In humans a good example is the long-haul flight where at the end you find that your watch and socks have made a deeper makr on your skin than usual.
This is why a lot of time spent in the field is useful as your horse is constantly on the go.
As far as reducing swelling goes you can cold hose before and after rides; however, this also provides an open invitation to various nasty fungal infections! Care must be taken to dry carefully... luckily you have a TB so you don't have to worry about feathers drying hell!