If I know that it will sit a while before I use it again I will do the outside with oil, it can't hurt. Especially my collectables. Just don't wash them with detergent.

You will get as many different opinions as there are brands of camp ovens!

In my opinion exterior surface rust on a camp oven looks unsightly but that could be because I'm used to dark oiled well-seasoned cast iron - shrug.   Surface rust on the outside of a camp oven is a nuisance because it stains your tea towels/oven mitts and anything else you touch.   

You only need a very light coating of oil to act as a moisture/oxygen barrier to prevent rust forming.  Too much oil used to wipe over a camp oven before packing it away may well lead to rancid ovens - puddles of oil could form in the bottom of the oven when the excess oil slides off the side walls.

For my cast iron - after washing I dry thoroughly over heat, then I use an oily paper towel to give the inside and outside a bit of a wipe over while it is still fairly warm, then put it inside my canvas bag once it cools down.  I don't think I have ever seen rust on my cast iron ovens once they are thoroughly seasoned - maybe because they don't sit unused long enough   

I once put away my new carbon steel Bedourie without wiping the outside with oil.  I had dried it thoroughly over heat but only oiled the inside.  There was a lot of orange powder [surface rust] on the outside when I got it out of the cupboard about 2 weeks later.

   Lesson learnt - oil all over! 
Now I dry thoroughly using heat, wipe lightly with oil, then put back over high heat to 'lightly season' before packing it away.   My 'blued' carbon steel Hillbilly doesn't seem to rust as heavily as the Bedourie, but it will if not oiled.

I don't know why carbon steel doesn't season the same way cast iron does but it doesn't make much difference to me because I heat dry - oil - pack away both types of ovens - I just use a tad more oil and a second bout of heat on the steel.


HTH
LG

only time we cooked a meal when the CO was rancid was when the CO was oiled and stored in a air tight plastic bin......the chicken went black.and the stink...putrid......didnt notice it till it heated up

It was canola oil.....bit too much when oiled to put away......only salution was to scrub it and re-season the CO.....after that we use canola oil spray thinly and wipe it dry then air before storing away in wooden box

a lesson learnt..... at first we thought the chicken was burnt........but it wasnt cooked...peeeeeeuuuuuu!!

Dave

After each use, I religiously coat my COs inside and out with either vegetable oil or animal fat. Furthermore when greasing, I focus equally on maintaining a good non-stick and water resistant patina on both the inside and the outside of the pot.  I particularly hate rolling out of my swag in the early morning after a heavy dew only to find fresh rusty residues on camp ovens which were left by the fireside from the night before.
Rusty pots are unsightly and with time and continued neglect, the rust may gouge deep pits, ruts or holes into a CO, which may seriously compromise the performance of the cookware. This situation is so unnecessary and wasteful, when it only takes a few seconds to oil a pot after each use.