Check any pneumatic tires for cracking, learn to read the manufacture date stamped on tires. Nice lady had her carriage gone over, fixed needed things. However no one checked tire dates because “they looked fine.” One tire went flat, started coming off in the show ring! Got her safely stopped, unhitched her Pair, carriage and equines out of the arena.
Upon examination later, tires were over 10yrs old, dry rotted sidewalls blew out without any noise.
Grease the hubs after removing wheel, cleaning bearings, wheel stubs. Clean old grease off the 5th wheel turntable if you have one, put on new grease. Check for wear on the kingpin, if you have a 5th wheel turntable. Also the bolt holding singletree/s in place. If there is any wear, replace the bolt with an EQUALLY hardened bolt. Cheap, soft bolts break and wear too easily.
Do you have brakes on the carriage? Fluid probably needs changing because the system is not air-tight, so moisture gets into the brake fluid. Most carriages use old car master cylinders which got rid of water-in-fluid just stopping car and heating up to steam off. Carriages never get brakes hot stopping, so water stays in fluid. Changing fluid is how you get moisture gone. Fluid SHOULD be clear tannish color. Anything opaque, coffee looking, has water in it. Get the PROPER brake fluid for your master cylinder. Older equipment probably uses type 3 and 4 hydroscopic, the older type fluid which absorbs moisture. The newer synthetic brake fluids type 5, are not supposed absorb moisture. Your local car parts store should be able to help you with this determination of needed type. Using the wrong type fluid will cause corrosion, deterioration of seals, O-rings, in the braking system.
There is a book by Dave Quist, available from Driving Digest, that covers carriage maintenance in great detail and other things you can do yourself.