BASS sells vinyl coated wire- I checked because I wanted to see if they might coat it with some other type of "plastic"... anyway, here is what I found on the dangers of vinyl:
What is polyvinyl chloride (PVC, vinyl)?
Polyvinyl chloride (PVC or vinyl) can be manufactured to be either rigid or flexible and is identified with the number 3. When flexible, PVC is used for medical bags, shower curtains, shrink wrap, and deli and meat wrap. The rigid PVC comprises 70% of all manufactured PVC. This is used to make construction materials such as pipe, siding, window frames, railing, fencing, and decking. PVC has been said to have had a major impact on improving life around the world.
However, there are claims that PVC poses serious environmental health threats. According to the Center for Health, Environment, and Justice, the production of PVC requires chemicals like the "highly polluting chlorine," the "cancer-causing" vinyl chloride monomer (VCM), and ethylene dichloride (EDC). They also claim that PVC plastic requires large amounts of toxic additives to make it stable and usable. These additives are released during use and disposal, resulting in "elevated human exposures to phthalates, lead, cadmium, tin, and other toxic chemicals." In 2000, the Environmental Protection Agency (EPA) proposed national standards to limit air toxic emissions from polyvinyl chloride production plants.
The FDA acknowledges that the building block of PVC, vinyl chloride, is a human carcinogen. They conclude that the amount contained in the PVC food packaging is within safe limits. In 2002, the FDA recommended that a specific compound used as a plasticizer in PVC either be labeled or removed from the medical bags in which it was being used. This compound, DEHP, had shown some toxic and carcinogenic effects in lab animals, but the effects on humans were unknown. The invasive medical procedures in which this was being used may have exposed people to DEHP levels that would exceed the amount determined to be safe in humans.
http://www.medicinenet.com/plastic/page3.htm
Our water is plumbed with PVC from the well to our house and yard (copper piping in the house) so both the humans and the rabbits have constant exposure to whatever is leaching from the pipes. I would think that the cumulative effect of that would have a greater impact than exposure to coated wire.