
When its rainy, windy, or just cold (or I really need my bacon fix!), I cook inside my 6X12 all the time! For breakfasts I fry bacon, sausage, eggs, pancakes/french toast, and make omelets. I heat/make soups, and grill hot sandwiches. I boil rice, noodles, and pastas to be mixed with other ingredients. (there's 101 ways to enjoy a pasta salad, and it keeps in the cooler!) Then of course, there's heating of canned veggies, soups, sauces, etc.
I open a window or two, roof vent or two (when not raining/snowing), and sometimes even the front door with the screen door closed. I pull out my Coleman propane stove and set it on top of my chuck box. It doesn't take much heat/flame for simple cooking/frying, and my co detectors have never gone off with adequate ventilation. I use a lid on pans when cooking greasy or splatter stuff like bacon, and cook it on a lower heat than normal to minimize any mess. Same with heating water for hot drinks. I don't have residual odors from any of the simple cooking I do.
I wash all the dishes/pans outside, regardless of weather. I heat the soapy water in them on the stove first, after wiping them out as a pre-clean. Water/drain/soap stays outside. In bear country, I wash/rinse everything over a bucket so as not to leave odors outside.
No deep frying. No heavy sauces/gravy. The key is to cook everything a bit slower, keep it covered as much as possible, wipe up any splatter immediately, and
ventilate! Be sure you stove is on a good stable platform with no flammables near it. Don't leave the trailer with the stove on! The stove gives out some heat, so properly ventilating even on a cold morning, it stays toasty inside, and the hot meal is a great start (or finish) to a cold wet day.