Are stolen items on my horse found by guards?

No. Items in your horses inventory are no longer safe with the new patch 1.3.3 (I have not noticed anything in previous patches).

I recently got stopped in town and the guard stole Han's Capons clothes that I stole from him. He left behind the lower value items that had already dropped there "stolen' tag, but took the main parts that were still labelled. (I loaded a previous save and they were 100% taken)

Not sure when this became a thing, but guards have always been able to "see" stolen goods in the horse inventory (as they make a statement about it), but now they can actually remove the items as well.

Yes, the horses inventory is safe from the guards prying eyes and yes, if you notice the guard before he talks to you, you can put your stolen items into your saddlebags and keep them safe.

While this method is pretty gamey, the guards recognition of stolen items is as well.