And I hope it develops as such, my party is mostly new positively aligned characters and over confident as well. They will most likely think the horse a silly omen or a random event.
All in all I plan to have four different horses (four horses of Apocalypse-ish) with different riders of all different abilities. This all begins after they removed an evil magical orb from a machine and I informed them they felt a little bit emptier. These assassins will be their "shadows", copies of their character sheets at the time beefed up a bit and created by the magic in the orb. Think the Dark Link from Ocarina of Time but now looking to kill them and take back the body they claim right too
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I think this is an awesome idea. Having a 'shadow rider' following your partyu wherever they go--but always one step ahead--is one thing, but eventually discovering that they're all basically evil versions of themselves is a wonderful idea. Especially if you're taking their character sheets and buffing them up a bit--it will cause them to really think about their own strategies and attacks when they're trying to defend against them! If played right, I could see it turning your players into even better players...
Are these riders literally twisted versions of the players, or are they just copies of them? If the former, you have a good way to tease them; show them just enough commonalities that they see something familiar, but play up the "twisted" aspect of the characters so they seem clearly evil and there's no gray area. This has the potential to be an emotional encounter for their characters, because they'll have to face things about themselves they don't like.
As for whether they'd just track the rider down, i agree with others in that you could always just make him disappear. The more aggressively they pursue him, the more easily he gets away. I also like moxcamel's idea of having the players lost the trail then get 'sidetracked' with a completely unrelated encounter. Make the players forget about it...then bring it up suddenly again. Make them want it, but don't give it to them...adds to the intrigue!