What size Mig welder would I need to build a trailer?
No offense intended, Fabsroman, but questions like this are exactly why people on the Internet respond poorly most times when somebody starts asking about building their own trailer. It's not like you came on here and said, "I have been welding pipe for 20 years, and I have decided I want to build a trailer." You don't even know the first thing, like what thickness metal you will need to use to build a trailer of a given capacity, and what size welder to use to weld that thickness of metal. It's not that people can't home-build trailers because OMG TEH LAWYERZ. It's that 99% of people who ask about building a trailer on the Internet are rank beginners who have not yet even built a welding table or a little shop cart or a BBQ or any of a zillion other projects that do not put life and limb at risk on the public roads--or, in your case, do not even yet own the welder that they would use to build the trailer.
Now, if I have misjudged you, then I apologize. If you are an experienced weldor who just doesn't know much about trailers, then you are the exception to the rule. But now you understand why people react so badly on the Internet when somebody comes along and starts asking basic questions about trailer building. It's because, if you have to ask basic questions about trailer building on the Internet, then you're not qualified to build a trailer. It's not about fear of prosecution or civil action, although that's not out of the question. It's about fear of killing somebody, or maiming them, or wrecking their car. I think we can all agree that those are bad things, to be avoided, even if no legal action results from them.
I'll now answer your question, just to show I'm a nice guy. The size of welder that you will need will depend on the thickness of metal that you want to join. The thickness of metal that you will be joining will depend entirely on the type and size of trailer that you're building. Before you can really answer the question about the thickness of the metal, you'll need to get a set of plans, and the plans will specify the material to use to build the trailer. I think that you would probably be safe getting a MIG welder in the 160A range, which should handle up to about 3/8" material. However, it's usually the case that manufacturer's specifications are a little bit "optimistic" on the single-pass material thickness, so you might be happier stepping up to the 200A range, which gets you to 1/2" material thickness, and which should do anything you will need to do on a trailer. Another advantage of a higher-output welder will be higher duty cycle at lower outputs--in other words, you will get better duty cycle running a 200A welder at 160A than you will running a 160A welder at 160A.