I always cook in my Scamp
and rarely, if ever, cook outside. I notice on occasion a little moisture on the under side of the cabinet but the cabinet is not hot. I too have the window over the stove. It is always open unless on the road. I have the fan overhead but rarely need to turn it on for cooking. I generally only use the fan when I'm cooking something a little fragrant, like broccoli.
No need for a hood. It would just take up room. The trailer has a more open feel without one.
Oh, I put a piece of linoleum on the wall behind the stove as a splatter guard. I simply cut out the hole for the window and shoved the linoleum under the upper and lower cabinets. I did have to trim a little for each rivet in order to get an inch or two behind the cabinets. It bludged out a little because of the carpeting. I solved that with a couple of pieces of the white trim the factory uses on the cabinet openings. I had some left over from a mod I had made.