Hi Jason,
These days there are several brands of products and varying techniques out there to wash your car in the waterless or (no hose way)
If you use your Mustang as an everyday driver, then yes, it will attract a fair amount of dirt and road grime on the car depending on road and weather conditions when you drive around. In my case, my two Mustangs only get driven on weekends for small cruises out and about. I will never take my cars out driving if the weather looks like rain or is or has been raining. The worst case scenario is when it has not rained in your area for some time and the roads are dirty and greasy. Then, a small to moderate amount of rainfall comes down to turn the roads into a dirty mush bowl. This dirty mush then gets flung up by other cars and trucks and transferred onto your car when you drive around in these conditions. This road grime or filthy road mush gets deposited on your car and gets into just about every crack and crevice - not good at all and very hard to clean properly.
Also, i never use a garden hose or pressure washer to clean my Mustangs. What David has said in his posts is very true. These old Mustangs tend to have water leak issues in one way or another. The last thing you want to worry about is any water finding it's way into the cabin or floor of your car. That is bad news for rusting out issues and smelly, mouldy carpets. It's the same for your trunk areas. David is correct again when he says that these cars were not dipped back in their manufacture days, and so there are hidden or unseen areas that never got coated properly and are susceptible to rusting out. The problem is that when a car gets dirty from normal driving around, it gets chemicals and acid rain lodging on the surface of the car. This happens more so when you live in big industrial cities and air planes flying over head all the time. So when you go to wash your car with a garden hose, you are letting these acids and chemicals wash into all the cavities of your car.Over a period of many washes and time, you will end up getting residue deposits and build ups of these chemicals or acids. They then act as accelerators or promoters of rust in all your inner panels that would not have any proper paint or anti rust coatings on them. It's the same with using straight detergents to wash a car with. They contain chemicals like phosphates in them that actually act as accelerators or promoters of rust in your inner panels. That's why i always recommend using a good quality wash and wax product if you insist on washing your car with a hose. It helps solve this very problem.
In my case, the basic technique i use for my Mustangs is to use either a soft feather duster or a compressed air blower gun and first go around the whole car and dust off or blow off any initial dust or dirty residue. Then i will use a good quality wet chamois (not dripping wet) and gently go around the car, starting from the top and working my way around the car as i go to the bottom areas last. Don't apply too much pressure when doing this process. Also, go to the trouble of washing out your chamois after wiping off one or two panels only. This helps prevent any scratching of the paint and also transferring dirt back onto the car that you have wiped off. You can the use a microfibre towel to follow through straight away to buff up and dry the surface. I like to use a quick detailer spray wax at this point to apply a wax coating to the paint to finish off with. You move in and wipe off and buff off the detailer with a microfibre cloth to bring up a lovely finish. The name of the game is to try and minimize the possibility and not scratch the car's surfaces. If you go about it carefully and use the above techniques, you should not get into any trouble in that regard.
There are other products and techniques out there that are available to make use of. Here are a few references to go with -