Was the cause and recommendation for treatment identified?
Hornbeam, as a tree name is commonly used for two trees, both native and at the top of their climatic range, commonly called the Carolinian Forest, along the lower great lakes.
The first tree is commonly known as Hop-Hornbeam (Ostrya virginiana) and is easily identifiable when mature by the linear stripping of the bark. The fruit grows in a cluster, and is very similar to the fruit of the vine, hops, hence the name.
The second tree, also an understory tree in the Carolinian forest along the lakes, is the Hornbeam, Blue Beech or Ironwood (Carpinus carolinianus). The latter name is for it’s hard wood. It’s fruit is a nut at the base of a three lobed leaf-like structure. The most notable field mark for this tree is the bluish, smooth bark, arranged in muscle-like ridges which is very different from the Hop-Hornbeam.
Both trees have been described by Cornell University as relatively pest and disease free. It is always helpful to know which species is being discussed. Using the scientific name, in addition to the common name is important in cases such as this.
By enlarging the original photo of the twig from the January 2014 question, I can see that the spots are indeed fungal, but cannot be 100% certain that it is anthracnose. Further investigation into the Master Gardener website did not reveal more information regarding this question. However, the recommendations made in the link to Cornell University Plant Disease and Diagnostic Center in the original posting are still sound. I checked the National Arborists (American site) for anthracnose disease, and their recommendations for disease prevention is comprehensive.
Even so, treatment for anthracnose depends on the tree species, as much as proper identification. The latter site recommends professional assessment and treatment. Particularly if you are located in Toronto, by-law restrictions would likely prevent you from treating with fungicide yourself.
My recommendation would be to get an on-site accredited arbourist to properly identify your tree, assess the disease, and recommend treatment. In the meanwhile, follow the clean up procedure to minimize spore development in and around your trees.