Is the stream a foot or two above where the trough will go? If so, it shouldn't be too difficult to put a pipe in the stream so that water flows down to the trough under gravity. Then you could either let it overflow constantly back into the stream, or you could install an overflow pipe at a lower level than the inlet, and let that constantly overflow back to the stream.
So it should be easy enough to do. I agree with the others that it might not be *worth* doing though, unless you also fence off the muddy bits.