Hello again Emily. I see a metal rod hold-down on that last picture of the battery that you just posted. If there is another one over the other battery and it too is anchored to the battery tray that you say is welded to the tongue, then I think the batteries are secure.
Note: I just looked carefully at an expanded view of the batteries in the first picture, and I see the second hold down rod on the far battery. They look secure to me.
The plastic covering you see on the battery cables is really only protection against sunlight. It's usually used to "bundle" multiple wires together and make things neat. It doesn't do a lot in your case and it does not hurt anything.
In their current configuration, if they are secure, I don't think you really HAVE to cover them. A cover would only protect them from an accidental drop of say, a wrench that would simultaneously contact the positive and negative terminals of one of the batteries. This would give you a "dead short circuit" which would be a HUGE spark at the contact points and would possibly melt the wrench or cause a battery to overheat and explode. I'm not trying to scare you with this, but that is really the purpose of a battery box or cover - to protect the battery terminals from accidental contact with metal things.
You can buy, at automotive stores, plastic covers that protect the terminals from that kind of contact. They come in red and black, red for the positive terminals and black for the negative ones. They are very inexpensive. But, you would have to disconnect each cable from the battery to slip the covers over them because that's how they are held in place. If you are not comfortable doing that, your garage mechanic would probably do it for a nominal fee. If you look in your car, you'll probably see covers like I'm describing on its battery terminals.
It might be possible to put a plastic box over the batteries, if you can figure out how to hold it in place and you can find one that would cover both batteries. It does not have to fit "snugly", but it does need to be secure. As long as it is not air tight and it covers the terminals, it would provide the same protection. Really, anything you can fit over the terminals that is NOT electrically conductive would do the trick. You just want to prevent any accidental metal to metal contact between the positive and negative battery terminals.
The term "vented", just means a container that is NOT air-tight. Batteries give off a small amount of hydrogen gas, and this needs a way to escape to the atmosphere.
- Jack