I stumbled upon these teachings of the Prophet Muhammad:

In a hadith narrated from Hazrat Ibn Umar (R.A) in which our beloved Prophet said "Teach your children swimming, archery and horse riding". In Sahih Muslim, the Prophet (s) said, "Practice archery and horseback riding." The Prophet (s) said "Any action without the remembrance of Allah is either a diversion or heedlessness except four acts: walking from target to target (during archery practice), training a horse and learning to swim." (Reported by al Tabarani on good authority) -- Sunnah Sports

Horse riding is an almost forgotten sunnah of our Prophet. -- A Productive Hobby: Horses and Horse Riding, The Brunei Times (pdf)

(I presume this is a sahih hadith; it's mentioned frequently online.)

Question: What is the modern-day applicability of "teach your children... horse riding"?

Essentially, should parents be putting in more effort to teach their children horse riding? It's quite an expensive hobby and I'm unsure of the benefits of it in the modern world.

There's a hadith

...when I command you about a thing out of my personal opinion, keep it in mind that I am a human being... (sunnah.com)

so horse riding could simply be a hobby of Prophet Muhammad, and we needn't worry about teaching it to our children.

(Image source: Nevit Dilmen, Wikimedia Commons)