I don't plan on hauling 2 cords of wood, I don't even burn wood. I may go haul some wood if we get an ice storm and haul away some some brush and wood and clean up for people. I mainly will use it to haul my sub compact tractor John Deere 1026 with brush hog or blade and FEL. If the axles are rated at 7,000 pounds I think that would be enough to haul a car if needed to be.
Ok... Your comment about hauling wood could have been taken a couple of different ways, but you're looking on the "smaller scale" end... No worries there.
Keep a couple of things in mind: Each axle on a 7k trailer will probably be 3500 pounds, possibly slightly higher - you'll want to look for the GAWR (gross axle weight rating) to know for sure. The trailer has weight, and you have to deduct that from the GTWR (gross trailer weight rating - think "7k") to know how much cargo you can legally / safely carry. In the case of a 7k trailer, I think you will find it common that the trailer itself weighs somewhere around 1750 lbs. Call it 1800, and plan on 5200 available for cargo.
Anything you put on the trailer, like adding a wooden deck (I did that with a utility trailer I had), is part of the cargo. So, are chains, binders, a spare tire, etc. Nothing by itself seems like much, but it can add up.
The 1026 shouldn't be an issue for you, even with a loader on. Depending on other attachments, like brush hogs, you *may* find that 16' is not really long enough. For example - my tractor measures about 15' from tip to tail with the loader installed, pallet forks on the loader, and a
ballast box hanging off of the back. In order for me to load that weight properly and get it placed correctly over the axles, a 16' trailer is too short. I personally needed the extra 2' of length for the trailer so that I could get the main load of the tractor over the center of the axles. Also - you could potentially tie down another attachment or something in front of the machine with a longer trailer and still be ok.
If you're going to be hauling something like a 4x4 Jeep (i.e. Wrangler), know that those things weigh quite a bit. Plan on somewhere around 3750 for a 4x4 Wrangler with a 6 cylinder engine in it. With that sort of weight on the trailer, you'll be quite happy to have "splurged" the extra $100 and gotten brakes on *both* trailer axles. Overall length on something like a Wrangler is in the 13' - 14' department, so a 16' trailer would likely suit it fine.
The one thing that I like about my equipment trailer that I didn't care for on the utility trailers that I had (and on a lot of landscape trailers) is the deck. My equipment trailer has a solid deck and the others were expanded steel (mesh-like). The expanded steel helps keep the weight of the trailer down, which is great for the smaller axles, but it doesn't hold up over the long run to heavy weights like a solid deck does. That's a big part of why I installed a solid floor on my old utility trailer.