No, he doesn't. Uther doesn't arrest Arthas because he does not, at that point, have any actual grounds to do so yet and was likely still hoping Arthas would reconsider. That doesn't make Arthas outrank him, though. It's also questionable whether Uther even has the rights to arrest anybody unless ordered by somebody who does.
Being heir to the throne does not actually give him any direct authority until his father dies, and we don't know what, if any, further titles he had at the time that would have done so. He's the prince and heir to the throne, not the ex-prince and current king.