Let's be clear, this isn't the window or through the wall unit that's too difficult or heavy to remove. These should be covered during the winter to help prevent heat loss. I'm talking about the units that sit outside, connected to the house with a wire and line set (the plumbing that carries coolant or refrigerant in and out of the equipment). The most obvious reason is that homeowners want to keep leaves out. I've even had one customer fabricate a wooden "roof" to keep the icicles from smashing it to bits. Still another insisted on wrapping everything with non permeable plastic because he swore it was raising his heat bills (that guy was a few tacos short of a platter, but I digress).
I'm not going to beat around the bush. Covers are a terrible waste of money at least and will destroy your air conditioning system in one season. If the cover doesn't breathe, condensation will bead up inside in the winter and rust it out. I found this out the hard way on my own outside unit when the bottom was completely rotted out. The compressor was nearly sinking into the ground. If the unit you have is an air to air heat pump, a cover will ruin any efficiency trying to run it in the winter. Common sense would dictate otherwise, but this is getting so rare some believe it's a superpower. Accidentally running the AC on with a cover will cause the pressures inside to skyrocket, doing permanent damage to an expensive unit. In the case of the man who put the wooden roof on his, it caused a huge leak. Leaks are pricey and very time consuming to fix, even for seasoned technicians.
The other option is one you may not have realized, but one out of ten of my no cooling calls are the direct or indirect result of mice or other rodents getting inside during the winter. Since the cover shields the unit and keeps it out of the wind, mice are more than happy to build a nice warm nest inside the electrical compartment. Not only do they urinate and defecate inside, rusting out the frame and corroding electrical parts, their constant munching on wires can cause an open or short circuit. The result is a tripped breaker, blown fuse, a ruined transformer or control board. Damaged wires will have to be spliced or replaced as well as the corroded parts. Many new units also have circuit boards in that compartment; replacing them could be in excess of $500. The average service call is at least $300 to clean the mess and trying to salvage the damaged wiring.
So what to do about the leaves getting in? First and foremost, a few leaves inside aren't going to hurt these units. Next, these also need annual maintenance and cleaning. This should include inspecting and testing the electrical, cleaning the outdoor coil and all other accessible parts that do require disassembly. The temperatures going in and out should also be checked as well as filters cleaned or replaced (filters are usually extra). As long as there isn't a problem, the tech has no reason to put gauges on the system either (yes, I'm getting on a tangent). You will lose a very minimal amount of heat through conduction from the outside unit, but you'll lose far more just going inside and out on a typical winter day. They're also built to stay outside and even the lowest end ones have very durable finishes that can take the punishment as long as they can dry off. Even the motors are protected from the rain, snow and sun, and the patina of rust on some of these parts will not affect the operation. Besides, if Junior decides to play with the thermostat in the winter with no cover on; no harm done other than it freezing up a bit. Conclusion: covers are best for humans, not for air conditioners. Maranatha!