Natural horizontal gene transfer in higher animals is possible, but still very rare.
If any transfer happens then it's usually from micro-organsims (viruses/bacteria) or parasites to the host animal (or the reverse). Transfer of genes from any other source to animals is almost unheard of, because the transfer needs to affect the germline (sperm / eggs) to last more than a single generation and anything that doesn't live inside an animal is unlikely to get there.
Therefore your example of getting GFP (or any other fluorescent gene) into a sheep is highly unlikely$^1$, even with a 1000 year timespan.
You'd need a virus or bacteria that has a fluorescent gene and naturally infects/lives in/on sheep. However, no natural bacteria or viruses have a fluorescent gene in the first place (they almost all come from corals or jellyfish). Another problem is that just having a fluorescent gene somewhere in the DNA, doesn't mean the any part of the organism is fluorescent; once its in the gene pool this should be achievable by breeding though.
- You'd have to wait for HGT of a fluorescent gene from a source animal/life form to bacteria. (Time estimate is super hard, you can maybe house some of these jellyfish in a fish tank regularly sequence the bacteria that live with them to see if HGT happened.)
- Then the genes needs to be transfered to a bacterial/virus strain native to sheep (This is relatively easy/fast, since bacteria are quite proficient at HGT between each other)
- Lastly you need a 3rd round of HGT from the bacteria to the germline of the sheep. (Again this might take 'forever': most mammals don't like bacteria or viruses living in or near their reproductive organs. Also at least from this point on animal experiment laws will become a serious hurdle to your project).
1) This is a researchers highly unlikely: without trying this, its not correct to say impossible, but the chances are so low that for all practical purposes it might as well be impossible.