Shadowfax would never be tied up at a picket. He was wandering free, and the other horses sensed his presence and went to him. I don't think Saruman had anything to do with the horses deserting the Three Walkers.
Well, on second thought; maybe he did, but I bet he never expected them to find Shadowfax, and wind up coming straight back to their riders! (That was always Saruman's weakness, always underestimating smart creatures like Shadowfax and Treebeard.)
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