Your question puts the proverbial cart before the horse in a few ways, so to speak. Your shortened answer is at the end.

Really, there is no clear answer to your question, because some of the evidence we need to know for sure either does not exist or has not yet been discovered. Also, your question isn't really possible to answer because its core assumption is wrong.

Based on the evidence, current scholarship suggests that horses were used in warfare before they were used in a "work" setting, and before that, they were used more as livestock that were herded and kept for milk/slaughter. Again, we don't really know this, because the cultures that had horses first also didn't really keep a lot of records.

But at any rate, we know reasonably well that chariots started appearing somewhere around 2000 B.C.E. Chariots were used primarily for human transportation. This differs from standard "work" in that the horse/chariot system at the time was really not appropriate for heavy work, like hauling or plowing. Due to limitations in technology, like the lack of an anatomically friendly horse collar (load bearing part of the harness that the horse pulls against to move the cart), there was something of a weight limit to the chariot. Basically, with many types of harnessing, if the horse pulled too hard against it, it would restrict the horse's airway, suffocating it as it worked. So, a smaller chariot might be able to pull 1-2 men effectively without suffocating the horse with the harnessing. Due to differences in anatomy, draught animals like oxen were able to pull loads better than horses at the time. Horses, however, had the advantage of speed, which oxen are not famed for, and a single horse is often considered stronger than a single ox. Horses are also somewhat more temperamental than oxen, making the ox a more economical choice.

During the time of the chariot, horse riding didn't really exist (people probably tried and failed a LOT), and so "cavalry" didn't exist. Horse riding took another few hundred years (for breeding/training to develop in the correct ways), and started becoming more common throughout the Eurasian steppes, where it spread in all directions.

So, we start seeing things like light cavalry and horse riding existing around 1000BC-700BC. But as effective cavalry? Well... that depends on what you think effective cavalry actually is. Greek cavalry functioned mostly as skirmishers, but they were not the bulk of an army, and they were definitely not used for heavy fighting. Roman cavalry functioned in a similar way.

And yes, people probably used some horses as pack animals, but horses in all areas were far too expensive to keep for mundane uses like packing supplies- horses require lots of care, grass, and had needs beyond that of an ox. Again, the horse is stronger, but the ox is more economical.

Really, I'd say that cavalry was not truly effective militarily until the advent of the stirrup and coupled with the lance- only then could cavalry really compete with the military efficacy of heavy infantry, which was probably somewhere around 800 A.D. (In Europe, at least. Bite my shiny-metal-European focus, at least until I can do some more specific research on the time frames of Chinese horsemanship....)

And it wasn't until the invention of riding and the stirrup that horses were bred large enough to actually "work" in a useful context, and even then, the anatomically correct horse collar didn't spread to Europe until somewhere between 900-1200AD, well after the stirrup became more widespread.

Horse became useful for work when horses were bred large enough for draught, and then it still took a while for people to decide that horses were faster at ploughing than oxen. Even then, many people remained in favor of ox teams, because ox teams were cheaper and easier to maintain than horse teams.

So, I'd say people realized the agricultural potential of the horse somewhere around Central Europe, between the years of 1300AD and 1500AD, after having used the effectively as warhorses for a few hundred years.