Cooking outside is fun, except if you permanently force yourself to do it for each and every meal.
We cook both inside and outside, as our mood fits us. Haven't noticed that smells linger after a short while. As others have said, open the windows and use the stove vent and fans.
Our philosophy is this: We bought a trailer with a lot of amenities, it is ours and we intend to use them. I've never understood folks who purchase a trailer but then don't use the toilet, or don't go #2 in it, or keep their used toilet paper in a basket instead of flushing it, or don't cook on the stove, or don't use the shower...or whatever. It is their choice and they have every right to do or not do as they please, but I'll never understand it.
These may be the folks that have plastic covers on their furniture at home. :)