No, it doesn’t give him the ‘right’ to verbally abuse you. But he does have the privilege of being in a society that allows for relatively open and unrestrained discourse between people. As long as he doesn’t overstep the bounds of what the law requires, he can be upset about something and express that dissatisfaction accordingly. It doesn’t mean he’s right, or that you have to listen to it.
Social courtesy might indicate that you should place your sprinkler so that it doesn’t wet his property. However, there is a difference between getting a caravan wet - which as you pointed out sits outside in the weather anyway - and getting something wet that could be actually impacts by some water (e.g. a freshly painted fence). Also the type of water may be relevant - if you were using bore water that might stain whatever it falls on, for instance. None of that is apparent here, I’m just giving some rounding to the potential situation. What could be directly relevant is some particular aspect of that caravan at that moment which would indicate that a fear of rotting is relevant; such as him working on it in otherwise fine weather to repair/restore something where water penetration is a factor. Again, I don’t know, but in the absence of that sort of factor it would certainly appear his conduct is unreasonable. It doesn’t mean he doesn’t have the ability to act that way. There are often consequences to being unreasonable, but in the situation there is no obligation to be reasonable.
The question becomes, at least in my mind, why is he acting this way? Is this simply the latest in a long string of unreasonable behaviours? If not, what has caused this? It may be that his reaction to the water on the caravan is an outward sign of something else that’s going on in his life causing him stress. It may not be about the water at all. There may be something going on in his life that he’s merely reacting to. If he’s usually a cantankerous old goat, fine. If not, it might be worth making peace, apologising for the sprinkler (without acknowledging his argument), and asking if everything is okay - not because you’ve necessarily done anything wrong, but because you are neighbours and it is in everyone’s best interests that you both get along.
I think the simple fact (and tragedy) is that people go from 0-100 on the aggression meter too quickly. Stop, take a second, and find out what’s really going on. If it really is war, then fine. If it’s not, then having a cooler head about things can stop the situation progressing to a much harder, and more stressful, situation to deal with.