"Trailer" means different things to different people.
There are "camper" type trailers that attach in under an hour to a truck and roll away.
There are single wide, "manufactured" homes which are attached to a cement pad, and are expensive and difficult to move, and are hooked up "permanently" to water, electricity, etc. Older units, before say 1995 are much worse quality.
There are "double wide" manufactured homes. Same thing, but even bigger. Very permanent, since the two parts get joined. The defining noticeable thing about these is they are 1 story, and usually longer than wide. But, you might not notice what it was otherwise.
I grew up in a double wide on a very rural lot. It was poorer quality than "high quality" homes. It was better quality than crappy quickly built tract homes. It was quicker to build, and cheaper because of the location. It took about 3-weeks to move the old 1970's single wide trailer, finish the plot, and put the new one in. "Stick built" would have meant my family spending months someplace else, and paying mileage for all the workers for that time too. I think it was a mustachian choice!
So, a camper would be fun, tiny house style. It would have insulation problems, sure. However, you wouldn't HAVE to be in a "trailer park." Or anywhere really! If you didn't like it, you could move!
All of the "downsides" of a trailer are the same as an apartment-they depend on neighbors, construction quality, and size to be safe and pleasant.