Timoney says it depends on the conditions. I don't think you could come up with a percentage because these diseases are opportunistic. Outbreaks happen when the conditions are right, not just because the pathogens are present, which makes occurrences hard to predict. Geography plays a big part. So, it depends on what part of the country and even the time of year.
Weather can also affect transmission of diseases from other animals to horses.
In horses, the disease caused by C. pseudotuberculosis is known as dryland distemper, dryland strangles, or pigeon fever. Despite the name, pigeon fever has nothing to do with birds. This disease is common worldwide in sheep and goats, but the bacterium can infect cattle and other animals. Direct and indirect contact influence a horse's risk of getting a disease from another animal. Timoney refers to this as opportunity for transmission.