To winterize or not winterize has a lot to do with where you live & where you intend to pull the trailer in winter.
I would at the very least make sure I had either blown all the lines out or pump some anti freeze through the water pump and dump some down the sink drain as both can hold water. Know of way to many instances where someones first trip of the spring has been interrupt due to the need to go buy a new water pump as theirs was not winterized properly during the winter.
I live in an area that historically has very mild winters by many peoples standards. For example the City does not own a dedicated snow plow and flowers are blooming by February. :-) Last winter for example I could have very easily gotten away without winterizing the trailer BUT mother nature has been known to throw a curve ball or two. LOL We have winters where the temps have gone well below freezing into double digits and stayed that way for a week or more. Mother Nature also likes to throw a wind storm or two at us, knocking out power - which means that heater in the trailer is not going to be working - we can go without power for a number of days as a result. What happens in that situation if the temps also fall
With the wind comes the added issue of windchill factor. In those situations a thin wall of fiberglass and thin layer of foil insulation is not going to stop items inside the trailer from freezing particularly if the trailer is not moving so the liquids are not moving. If your going to be towing through areas with freezing temps keep the wind chill factor in mind in those situations as well, as the heater in the trailer is not going to be on then either.
For example, one year coming from the South in December (I know going totally the wrong way at that time of year - was not my plan) the temp reading inside
the trailer when I pulled into Champoeg State Park near Portland Oregon for example read 10 degrees below freezing & the park itself had a nice thick layer of frost across the grassy areas.