General Wear and Dirt
Over time, especially if left outside over winter, your barbecue covers will need cleaning. At first it may not seem like much of a need, but, without regular cleaning, that grit will build up. Wiping down both the hard metal cover and the cloth coat will preserve them much longer than doing nothing. Remember, your barbecue is exposed to heat, cold, rain, sun and wind. If these elements can wear down roofs and walls, they can wear down your covers as well.
Soot and Smoke
On your metal cover in particular you will need to regularly scrub out the soot and built-up carbon from cooking. This will build up on the inside cover as a black, ashy film that is also oily. It is essentially the burned smoke that comes off your food as you're grilling. Failure to do so will cause your barbecue grill to cook hotter than normal in odd spots and areas. It will also build up residue that will eventually fall down on your next cooking meal, adding unwanted flavors to your meal.
Animals, Bugs, Mold
Just throwing your cover on your grill at the end of fall and not cleaning underneath is a bad idea. Leftover grease, food, carbon and other remnants are a wonderful meal for small animals and bugs. Many a barbecue owner has found their unit invaded by ants savoring leftover barbecue sauce drippings for weeks at a time. One odd fellow found a beehive making itself at home.
Mold is also a problem. Cold creates condensation on metal and a cloth cover on top blocks out sunlight. Add grease and old food and you have a great environment for mold to set in with moisture and rotting food bits.
Your metal cover is essentially made of steel, which will rust after its protective coating has been broken, chipped or scratched. Add the condensation of winter, and oxidation can do a serious number on your metal cover. The result is a rusty mess that you don't feel interested in cooking a meal under next summer. Spraying a bit of cooking oil on the cover hinges, inside and the grill itself will fend off moisture and rust.
Use the Right Cleaning Products
Many cleaning products will cut through grease and carbon buildup easily. However, these chemicals can be very harsh and are designed to be used on hard services. The same chemicals that break down fat and dirt can also eat away at your cloth cover and the protective coatings on your metal barbecue cover. Make sure to check what a cleaning product may do before using it on your barbecue grill, or you may be in for a rude surprise.