Dangerous bacteria such as cryptosporidium and E. coli are both present on farm animals' coats, and both can sicken your toddlers if they ingest them. Cryptosporidium, for instance, can cause severe diarrhea that lasts up to a week, and E. coli causes fever, vomiting, and severe diarrhea.
In fact, E. coli 0157 — the strain that caused a rash of poisonings a few years ago when kids ingested it in hamburgers and unpasteurized apple juice — can be deadly, and every year up to 100 people in the United States die from it.
Farm animals get the bacteria on their coats when they stand or lie in their own or other animals' manure, as penned animals at petting zoos, traveling fairs, and similar exhibits tend to do.
That's why the Centers for Disease Control has posted information about the risk of bacterial transmission, not serving raw cows' or goats' milk, and keeping food and drink areas separate from petting areas.