I do not know whether running a farm has ever been considered the most prestigious kind of work, but it is certainly nowhere near as prestigious as for example being a doctor, at least in my part of the world. The exception is maybe if one runs a winery.
Why is it like this? Does it have historical reasons? If this changed over time, when did it loose its prestige?
I am mostly after a non-localized answer, but in case someone wants to know, my part of the world is Northern-Europe.
It may be different in different locations but it usually comes down to what Tom mentioned as the manual labor, those who work with their hands or outside do tend to lose some level of prestige in many cultures. In Europe in the Middle Ages if you worked outside you were of the lower classes, giving rise to the idea that tanned skin was a mark of those who did manual labor. Lighter skin was considered the norm for many nobility at the time. Some asian cultures have instances of the same values, where light skin in ancient Japan or China was desired, and if not available there was makeup to achieve the right effect.
You could say many manual trades are also not very prestigious, leather tanning, butchers or even bakers who have to work hard and with their hands often don't achieve much status. Unless you become able to own multiple places, and hire others to do the manual work for you, at which point you can become more respected but only so far as you can show you are able to make money - but then you also enter into a different class. Much of this also seems to come from the different social views of tradesmen, workers and any upper/investment/merchant class.
Even for wineries, taking your example, I am sure the vintners are given some prestige, but not the people picking the grapes or working the presses - the ones given some respect tend to be those who have some ability to impart. That knowledge makes them more valuable than just a pair of hands, so even a cheesemaker could receive some amount of respect if he was able to make very fine cheeses, but the person separating the curds is probably not going to get much respect as they are still considered a manual worker.
Actually RUNNING a farm has never been considered "prestigious." But OWNING one often has been.
"Farming" is connected with manual labor, sweat, etc. As such, it is not what social economists like Thorstein Veblen would consider "honorific." On the other hand, to be an owner is to be member of the landed gentry, and a member of the establishment.
Farming has been considered "unprestigious" when the owners were also the actual farmers. In the Middle Ages owners and farmers were not the same people.
Farming lost it's prestige in prehistory with the growth of organized warfare.
Organized farming began many thousand years before Christ in the fertile soils at the estuaries of mountain run offs and in the flood plain of rivers. Most such communities were initially organized into small scale villages with communal farming and later developed into city states. Now here I am talking thousands of years before the Egyptian Pharaohs.
Organized farming led to a population boom at the time and as a result cities grew massively, spawning off sister villages which in turn became cities. Excavated statues and figurines show that up to this time such people worshiped the goddess and were probably organized on a matriarchal basis, with women or communities having title to the land, with women actively engaged in farming and advancing the science of farming.
But with population growth came conflict and warfare which eventual led to the creation of minor kingdoms, with rulers controlling several cities and communities, together with their farms. At this point the ruling class consisted of warriors and priests who would own the land but never work it. The work that was considered important was the work of the warrior and the intellectual work of the priests. Together with this upheaval feminine deities were replaced by male deities and matriarchal societies replaced by patriarchal societies, with almost all positions of power were increasingly dominated by men. This then, the fall of matriarchy and women's status coincided with the fall of the value of farming.
This tradition then intensified and grew until the first empires were formed, and it was fully incorporated into all the major succeeding empires, including the Qin, Sassanian, and Roman empires. By this point, all manual labor, with farming its chief employer was considered beneath the ruling aristocracy. Consider also that much farming was carried out by slaves and serfs who were tied to the land and were considered property. The sons of aristocracy would then either become land-owning warriors or priests.
Later, when Europe began its universities around 1100 AD, most universities would only study arts, medicine, law, and theology, with arts being the lowest in rank, and even then mainly consisting of literature and philosophy. So enshrined in the university system was the thinking that any kind of manual labor was unworthy of a scholar. I believe this kind of thinking still persists to modern times, though much eroded, so for example, law is considered higher than engineering.
So despite the fact that agriculture continued to be the main source of wealth for almost all ruling classes well past the Renaissance, agricultural workers were looked down on, with many aristocrats holding to the view that manual laborers were lower humans, less capable of thought and emotion, and generally of lower inherent value.
In the 19th-20th centuries an industrial worker in a city (not to say a person of intellectual labor) could earn much greater money than an agricultural worker. This was a major driver behind rapid urbanization.
It should be noted also that technological innovations spread to the rural areas much slower than inside cities, thus making the farmers to look somehow "backwards". Also the agricultural work did not require any education except the traditional training. That even more worsened the image of a farmer who often was even illiterate.
