covering a/c unit outside?

This sounds like a split system heat pump. If it both heats and cools, it should not be covered. Window units are sometimes covered to prevent wind from blowing through the unit and into the room. TB

this is not a heat pump, I have a furnace inside the hom..this is a gray box and top of that says "Carrier" (I guess may be evaporating coil)

Some people seem to like to cover them. I don't. I suspect the manufacturers of the covers will all agree that you should cover them.

I know they sell enclosures, but that may just be a way for them to get your money.

I've read that having an enclosure will hold moisture inside and cause more rapid corrosion. It also makes a nice winter home for some animals.

M> someone told me that during winter and early spring when it is raining

That's the main reason my heating guy told me to cover it - but just the top, not the sides. Allows air circulation, but keeps stuff like pine needles and maple seeds from getting in there. I had it cleaned when I moved into the current house. It looked like a compost heap inside, and THAT holds moisture.