Like others have said, Ebay or Bitz Barn is the way to go. If you just search for "Warhammer Empire bits" or "Empire horse bits" you'll get a virtually endless list of sellers who sell off bits.
I was able to get a plastic boar and various different orc bits to make an orc baggage train. Cost me a fraction of what it would have if I bought new kits and bashed them that way.
As was said above, I also believe that the 6th Edition period was when they were using metal riders along with the generic plastic horses that they put in pretty much all their kits.
As a matter of fact, here ya go! Ten seconds of searching and I found a bunch of 'em. ***One thing to note is that during this time period, there were actually TWO(there was a third one for Bretonnian horses) standard generic horses GW put in their kits. One was the unarmored horse with the plain tack and modestly decorated saddle – the other was the heavily armored horse(which may have actually come in two versions, one more heavily armored than the other), with the spiked face piece and plate and chain mail all over it, which they used in some of their knights kits and possibly with some of their chaos stuff;
Some images;
link
If you look at these listings you'll see the distinct difference between the unarmored generic horse and the armored generic. For the Empire General I would guess that it originally came with the armored version, but I could be wrong about that;
auction
auction
auction
If I'm not mistaken, the horse in this Kislev blister pack was the standard plain, every day generic horse of that time period. It was used for Empire, Kislev, and also their wagon and baggage train kits. I believe you'll also see the same horse show up in some of their old and now long out of production Dogs of War regiments and personalities kits, like Midas The Mean, etc.
auction
Here is Midas the Mean with a very similar horse, if not the same exact horse;
auction
Here's an image of the generic armored horse with the face spike, this horse is mounted with a 6th Edition general I believe;
