I grill year-round too - I've even grilled in blizzards! Mild ones, anyway. I've been a regular Weber user (of the charcoal variety) for over 20 years. 
I wouldn't use chemicals on the actual grilling surface (aka the grate). It should be scrubbed with one of those wire brush/scrubby tools each time before you use it, and should be oiled (or better, sprayed with a non-stick charcoal spray) before you put it over the coals. Weber makes a spray that's safe to use even when the grill is on the fire. I've used it, and it works well. Since the grill is supposed to be hot before you put the food on, just put the grill onto the fire for a couple of minutes before you start cooking. That will sterilize it.
I took a look at Weber's website, and they recommend brushing the grate each time after cooking with a brass grill brush - after it has cooled down, of course. Personally I usually grill in the evening, so that's not practical. By the time the grill has cooled down enough to brush, I'm asleep. Still, brushing it each time before use has worked fine for me.
If you really want to try to get it to sparkle, you can use fine steel wool and mild soapy water. But you need to be very gentle. I really wouldn't risk it, myself; you could easily damage the surface.
As for the rest of the grill - the bowl and lid - they recommend warm soapy water (mild dish soap) and a sponge or dishcloth. For serious cleaning, "lightly scrub the porcelain-enameled parts with a soapy, fine steel wool pad. Be careful not to scratch the porcelain."
If you have a gas grill, you can look up specific care for some of the other parts at the weblink below.
Happy grilling!