Many people park their motorhomes in the winter. And of those that still use them, many do not cook in them except for perhaps using the microwave. This is understandable since cleaning up is more of a challenge without running water, using the gray tank and having an operating water heater, but it is not difficult with a bit of planning. Of course, if you are looking for an excuse to eat at a restaurant…
Here is how we do it in our Roadtrek. The cooking part is not much different, but we do try to minimize things that need washed. Paper plates and bowls we use year around (except for when we have guests), but plastic forks and spoons and paper cups are a nice winter accessory. Microwave in the bag vegetables also minimize clean up. For soup you can microwave in paper bowls vs a dish or a pot on the stove. So when dinner is over we may only have a skillet, a sharp knife and a serving spoon to wash. Although at breakfast there is the microwave bacon pan as well.
We wipe all food or grease off the items to be washed with a paper towel. We put about 2 inches of water in our collapsible bowl from the jug on the counter. We microwave it (assuming shore power or generator) until it is hot and with some dish soap and sponge clean all the items. Rinse them as best you can in the soapy water and pour the water into your dish pan lining the sink (that keeps water from going into the gray tank). Our collapsible bowl has a small handle and a pouring spout to make this easy.
Rinse the bowl and add some more water and heat it in the microwave. Rinse anything that fits the bowl in the bowl and then use the bowl to pour rinse water over the skillet or bigger items to rinse them (over the dish pan). Place them on the drying mat. Then dry all the items and return to storage. Microwave the dish sponge to sanitize it. Wipe out the microwave. Not too much harder than cleanup when you are not winterized. Most of the time you can broadcast the gray water in the dish pan in a snow drift.
If you don't have shore power or a generator, heat the water in a pan on the stove and do the same thing. Don't let cold weather keep you from using your RV in the winter. Winterizing doesn't mean the end of the season. You just need to adapt to the conditions.