There are many ways of conveying movement, here are just three example shots taken over two days on a recent trip to Yorkshire.
pic #1 an effective focal length (EFL) of 320mm 1/640 sec. The fast shutter speed freezes the water and the splash for the shallow water.
pic #2 EFL 210mm 1/25 sec. It is very difficult to pan slowly enough for horses cantering, a flat out gallop would have been easier, at least for me, having been used to panning to follow racing cars.
pic #3 EFL 500mm 1/500 sec but I had to be quick to catch it before he disappeared! The “footprints” still clearly suggest movement.