Wash the body of the trailer frequently. Road salt and other minerals can build up on the sides and bottom of the trailer, and will eventually shorten its life. Wash the trailer regularly, and ideally after every use in winter, with warm water and a sponge or a power hose.
Check the body work. Crawl under the trailer with a flashlight and screwdriver. Use the screwdriver to probe any suspected areas of corrosion. Any weak areas should be repaired immediately.
Check all electric wiring on the trailer. Note any damaged or loose areas of wiring, and make repairs, as necessary. Check the electrical system regularly by hitching up to your towing vehicle and testing brake lights and indicators.
Look at the tires. Note any areas of uneven wear, which could indicate problems. Replace the tires when the tread becomes worn, and keep tire pressures at the correct level.
Use lubricating spray on hinges, and to the area around the hitch. Check that all parts are moving freely.
Get your trailer serviced regularly by a qualified mechanic. Have him carry out a full inspection of the bottom of the trailer using an inspection pit, and look at brake lines.