Xanathar's Guide to Everything greatly expands on the use of tools. Here are parts of the section on Cobbler's Tools (p. 80):
Although the cobbler’s trade might seem too humble for an adventurer, a good pair of boots will see a character across rugged wilderness and through deadly dungeons.
Components. Cobbler's tools consist of a hammer, an awl, a knife, a shoe stand, a cutter, spare leather, and thread.
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Maintain Shoes. As part of a long rest, you can repair your companions' shoes. For the next 24 hours, up to six creatures of your choice who wear shoes you worked on can travel up to 10 hours a day without making saving throws to avoid exhaustion.
The book also expands on crafting an item as a downtime activity, and its requirements (p. 128):
A character needs to be proficient with the tools needed to craft an item and have access to the appropriate equipment.
If you are proficient in Cobbler's Tools, can its benefits (making both non-magical and magical shoes, maintaining shoes, etc.) also apply to Horseshoes? Or are shoes and horseshoes too different from one another?
Best Answer
No, cobbler's tools aren't used to craft/maintain horseshoes
A cobbler, by dictionary definition, works on shoes for humans. Traditionally, this would be primarily leather work.
Farriers do work on horseshoes. This used to involve both blacksmithing skills (to make the shoes) and skills for maintaining the animal's hooves. As such, smith's tools would be closest for horse shoeing in 5e. Certainly, if you really wanted to add this skill set, you could create a new set of tools with proficiency for farriers.
There is virtually no overlap in skills or tools between a cobbler and a farrier. Well, a cobbler does use a hammer, but certainly not in the same way.