Hardware - Check your hardware for smooth function and for cracks. Check everything from windows and walk-through doors to the rear doors and ramp. Tip: Regularly lubricate hinges and latches to keep them from "freezing" in one position, and to extend their lifespan.
Wheels & Tires - Your trailer tires should be in good shape, and that goes for both tread and sidewalls. Check the spare tire, too, in both your towing vehicle and trailer. Keep all tires fully inflated. Make sure that all the wheels' lug nuts are tight. Tip: Repack your wheel bearings at least yearly; more often, if your trailer sees a lot of use.
Hitch - Be sure that the hitch is on, and that the socket (if it is a pull-behind) is closed and locked over the ball. The hitch collar should slide easily and close completely over the ball. If the lock pin is missing, replace it. The ball should be no smaller than two inches, and might be larger. While you are looking at the hitch, be sure all the bolts are tight and none are broken.
Safety chains - Safety chains should be crossed and hooked to the frame of the towing vehicle. Be sure they are solid and heavy, with every link in good condition - they'll need to hold the trailer in an emergency. A hauling rig, like a chain, is only as strong as its weakest link. The truck frame, hitch, draw bar, ball, chains and trailer frame all must be able to handle the load.
Brakes - Check the trailer brakes and your brake controller. Some trailers have their own braking system; some don't. If yours doesn't, keep in mind that your towing vehicle is providing all of the stopping power for both your towing vehicle and your trailer. Be especially careful to avoid a sudden stop that could cause your trailer to jackknife. Do you have breakaway brakes? Check that the cable isn't snagged on anything and that it is long enough. You don't want it to over tighten and break, or pull the coupler loose if you have to make a tight turn.
Lights - Brake lights, turn signals and running lights should all be working. Check inside trailer lights as well. Have someone inside your towing vehicle test the brakes, then the right and left turn indicators. Make sure the lights on both your towing vehicle and trailer are fully functional.
Dashboard - Check your fluid levels. If anything needs topping off, from fuel to windshield washer fluid, do it now.
Windows, vents & doors - Open the windows and the roof vents and close the screens to safely provide your horse with fresh air. Look inside the trailer to be sure you have everything (water tank? tack trunk? saddles? broom?), then close the doors and check that they are truly shut.
Ramp & rear door(s) - Every once in awhile, someone starts to drive off without lifting the ramp or closing the back of the trailer. If you do a walk-around inspection before every trip, this won't happen to you.
Your horse - Don't laugh. Every once in awhile, someone gets to a trailhead only to discover that something important was left behind: the horse! Again, your walk-around inspection will ensure that you never unintentionally leave your horse at home.
Think professional - Take a tip from people who drive for a living. Commercial truck drivers will tell you that the driver is responsible for the rig. Whenever someone else - your spouse, parent, offspring or hauling buddy - helps you hook up or load up, thank them, then do your own final walk-around check.