I'm on another forum and a lot of guys wipe the outside down with the same cooking oil that they use to season the inside. I haven't tried it but they claim that it works very well but it has to be redone regularly. From the pictures I've seen it doesn't really look like it's coated with anything so it must be a really thin coat. All of their cookers are painted with high temp paint and the oil is over top of that.
I have coated my smaller smoker with vegetable oil over the factory paint. It burns off of the fire box fairly fast. One downside is dirt and leaves will stick to parts of the oil if they do not dry out and season up right away as the oil will be sticky. the colder spots on the smoker will not dry the same as the hotter spots.Overall it's not a bad way to go but it requires work to keep it looking good. My big trailer rig smoker is painted and that paint is starting to rust through on the fire box. Rust is going to happen and I just do my best to repaint what I can and not worry about it looking like it's been used.
I used a vegetable oil spray(PAM) on my old offset firebox. Just sprayed it on and did my best to wipe lightly into an even coat. This worked ok but, as mentioned, burned off after a use or two—I gave up. If you wanted to keep it that way, I would make it part of your routine and just give the entire pit a quick spray/wipe while it is still warm after cooking.
Keep in mind, you will get a lot of dripping oil on the ground as well. We put new pavers in and I made a mess of them in short order.