My vehicle came with a “towing package”, meaning changes to the cooling system and partial wiring (to the back of the vehicle). However, strangely enough this package include neither a trailer hitch nor the end electrical harness. Fortunately, these parts are not expensive so I went to the good ol' eBay and purchased them.

The wiring was a simple matter of following the instructions. The trailer hitch on the other hand is supposed to be screwed into nuts provided for this purpose under the vehicle. It sounds pretty simple, but the problem is that those nuts have been sitting underneath the vehicle exposed to the elements (including healthy doses of road salt in the winter) for some 4 years, and so were full of rust and who knows what other gunk. Advice to deal with this matter gathered from the 'Net includes the following:

1. Use penetrating oil (such as WD 40), let it soak some, then clear the rust with a wire brush. Many people claim this to be enough, but that was not my experience (I guess it depends on how long the nuts have been exposed to the elements).
2. Once a preliminary cleaning as above is accomplished (so that at the very least the screw can go in a couple of threads), play the screw in and out repeatedly until it screws all the way in.
3. If the above fails, use a tap to remove the rust and debris.

Here is my refinement of this advice. My experience shows that the first step is obviously a must, but contrary with what many people are saying will not solve the problem. The second step will work most of the time but it is dangerous (see below), so your first choice after the wire brush cleaning should be the tap. This is how the tap worked for me:

1. Triple check that the tap being used matches the nut! If it does not then it will positively ruin your nut. The run-of-the-mill tap and die sets do not come with the taps needed for my particular application, so I had to purchase them separately. If you can live with the long shipping time from China several Chinese vendors sell them for cheap on eBay; see for example this listing (this is where I purchased my taps, but it is to be meant as an example rather than endorsement). Check the fit before ordering, then against the specifications after receiving the taps, and also visually against the screw.
2. Liberally pour penetrating oil on the tap and inside the nut. Wait at least 10-15 minutes for the penetrating oil to penetrate the rust in the nut.
3. Use common sense in deciding how much torque to apply to the tap, but do expect considerable resistance. For my M12 nuts I used a 12-inch ratcheting socket wrench to drive the tap and I still had to apply some pressure. From time to time remove the tap to clean the crud and perhaps apply more penetrating oil. The cleaning should take some 5 minutes or less per nut (not including the wait for the oil penetration).

If for some reason you do not want or cannot use a tap, you can try using a screw to unplug the nut. This is however a dangerous process. Indeed, stripping the screw is a very real possibility, and if you do so consider yourself lucky since other outcomes include stripping the nut or breaking the screw in the nut, both of which will be very difficult to fix. This being said, both the nuts and the screws are pretty strong, so such an approach is possible for this particular application. In my case I used it for the two M8 screws since I was unable to fit a long enough arm on the M8 tap. I used at first the aforementioned 12-inch arm to drive the screw in but I got stuck pretty early in the process, so I switched to an impact wrench. That worked in the end, but I recommend extreme caution since stripping or breaking become very real possibilities:

1. Apply liberal amounts of penetrating oil, be patient in letting it soak the nut, and use a wire brush to eliminate as much crud as possible.
2. Screw in the screw by hand for at least two threads. If that does not work repeat the penetrating oil application and wire brush cleaning.
3. Use a manual wrench to advance as much as possible (but at least a couple more threads) and only then go to the impact wrench (if needed at all).
4. Don't just press the trigger and keep it there. Go in using very short bursts (two-three blows) instead. Always verify that the screw actually turns during those blows and do not try again if it does not; unscrew it instead, do some more cleaning/waiting for the oil to penetrate and try again. This is likely to take longer than the tap method so above all be patient.

The above information should be generally applicable. For my particular CX-9 I had to overcome one extra hurdle: the driver side nuts are easily accessible, but the passenger side ones not so much. You will find a box in your way, which happens to be the spare tire hoist. A flat wrench might fit in between the hoist and the frame, but forget about a tap or the torque wrench that will definitely be needed for the final tightening of the screws. I found that the easiest approach is to remove the hoist and put in back once the trailer hitch is secured on the vehicle. This would proceed as follows:

1. Remove the spare tire.
2. Remove the two nuts that secure the hoist underneath the spare tire just removed. In my case they were only moderately rusted since they were somehow protected by the spare tire, but apply some penetrating oil and allow for some soak time just to be on the safe side.
3. Remove the four nuts that secure the main body of the hoist. These are very rusty since they are directly exposed to the road salt and crud. Apply penetrating oil liberally, allow for ample soak time, clean the visible threads with a wire brush, and proceed very cautiously. The bolts are very soft and easy to break, and if you break them you have to weld new ones in which is definitely something you want to avoid…

Installation (after mounting the trailer hitch) is obviously the reversal of the removal. I was able to use the old nuts, but that may or may not be your case so have some new nuts available just in case.