Are the ribosomes specific for each organism
One can prepare rabbit ribosomes from reticulocytes (immature red blood cells), and by providing a few cofactors required for an active extract, create an in vitro system that will translate virtually any eukaryotic mRNA that contains the correct sequence determinants. You can purify mRNA from your cells or tissues of choice, or you can synthesize an mRNA in vitro using a DNA template and an RNA polymerase. Either of these will be translated in a nuclease-treated rabbit reticulocyte lysate.

IVT (in vitro translation) extracts can be prepared from virtually any source (e.g., C. elegans shown by Bob Edgar in Cell ~ 1984). So I would predict that horse ribosomes would be happy translating human mRNAs, and human ribosomes would be happy translating horse mRNAs. The experiment you described, placing a human ribosome into a horse cell would be difficult to interpret because the endogenous horse ribosomes would already be translating the endogenous horse mRNAs, and so detecting activity from one additional ribosome could be challenging (even if you could come up with an experimental approach that gets that foreign ribosome in to the cell).

The take home message is that ribosomes, in general, do not care where the mRNA comes from--because ribosomes, as far as we know, do not have a way of distinguishing "self" from "other".