Do horses get "childhood illnesses"?

Yes - strangles is most often seen in young/adolescent horses (I've joked that it is horse mumps because it causes lymph node swellings, but it's actually closer to strep throat, being caused by a bacteria in the same family). Like childhood illnesses in humans, young animals are more vulnerable simply because they have not yet been exposed. Strangles is very common in racehorses in training.