There are several difficult problems with using diesel in place of propane for a trailer.
The most difficult problem is that diesel appliances are not readily available in a size and configuration, and price point suitable for a trailer. For example, there aren't any diesel refrigerators, since the yacht makers use electric ones. While cooktops and ranges are available (DickinsonMarine.com - Marine Stoves
), they are expensive, and the ranges have sizes and clearance requirements that are problematic for a trailer install.
Parts availability is also a problem since these are specialty products that have an extremely limited dealer network in the U.S.
In general diesel systems are sensitive to fuel quality and age while propane systems are not. Diesel in the tanks and lines that is more than a year old can pose serious problems that require dis-assembly of appliances and burners to correct.
Diesel cooktops and ranges require outside combustion air and exhaust while propane ones do not. Some diesel appliances are set up for gravity (rooftop) venting which means that the exhaust stack uses up valuable space and adds to the complexity of the installation.
In general diesel systems perform poorly in extreme cold because the fuel viscosity changes and will form wax or gel. The problems start at about 20 degrees for petroleum diesel, and at higher temperatures for biodiesel. There are ways around this but they add cost and operational complexity. You can use #1 diesel but it has a much shorter useful life and isn't readily available year around. There are tank heaters, but they require electricity. There are fuel line heaters, but they don't address gelling, only filter plugging.