Generally speaking, people during the period of the Year Without A Summer did not correctly identify the reasons for the year's unusual weather — though there are a few exceptions!

For background, the enormous cloud of ash caused by the 1815 eruption of Mount Tambora contributed to major weather changes across much of the world. In France, for example, there were days in June, July and August where the daily high temperature didn't reach 60º Fahrenheit (15º C) in Paris. Those were outliers, but the entire summer was colder than normal.(1) On top of that, it was also rainier — a dispatch from the French interior ministry noted "the abundant rains which have fallen for several months, and the overflowing rivers which have followed them."(2)

The weather in 1816 had tremendous consequences, beyond the thermometers of scientists and hobbyists. It devastated crops around the world and especially in Europe; with some experts at the time estimating that 1816's harvest was no better than half the volume of 1815's.(3) Since peasant farmers at the time often produced only small surpluses in the best of times, this led to famine, which led to crime, riots, and even veritable insurrection in late 1816 and early 1817.(4)

So what did experts think was causing all this remarkable weather? The eminent minds of the time put forward a few interesting but incorrect hypotheses.

The most common explanation may have been sunspots. In 1816, throughout the spring and summer, skywatchers noted that "large spots were visible to the naked eye" on the sun, "particularly at sunrise and sunset." Many people observed these sunspots and the cold weather and drew a connection — sunspots blocked the heat-giving rays from the sun and thus cooled the planet. The sunspot theory had its skeptics, however, including people who noted that some of the coldest days were associated with declining sunspot counts.(5)

Other people, confusing cause and effect, noted the large number of icebergs visible that year, and thought that ice contributed to lowering the earth's temperature (which it does, somewhat, though by reflecting the sun's rays, not by absorbing them as contemporary experts believed).(6)

French conservatives advanced another culprit that we now know can effect climate but wasn't to blame for the Year Without A Summer: deforestation. The ultra-royalist Marquis de Castelbajac said that France's southern departments were "devastated every year [by storms] since the plundered peaks of our mountains saw the passage of revolution." Royalists like Castelbajac were particularly focused on forests for political reasons, as his reference to revolution suggests — the French Revolution had seized forests from the Catholic Church and some nobles, creating new nationally owned forests. The right wing wanted to return those lands to their original owners, while their opponents wanted to use those forests as assets to benefit the country as a whole (including selling them off to private businesses to raise money to pay France's post-Waterloo war indemnity). But as part of this fight, conservatives laid out broader environmental themes. "Everywhere that trees have been cut down, man has been punished for his improvidence," the politician, author and world traveler François-René de Chateaubriand said in an 1817 speech to the upper house of the French parliament. "I am better equipped to speak on these matters, dear sirs, and on the consequences of the presence or absence of forests, since I have seen the pristine lands of the New World, where nature is newborn, and I have seen the deserts of old Arabia, where creation has all but died."(7)

Then there were the wilder hypotheses. A lunar eclipse on June 9 was supposed to have deflected Earth's winds, changing the weather. (This idea had some intellectual heft; the scientist Jean-Baptise Lamarck, best-known for his theory of evolution, had in 1798 published a paper arguing that the gravitational pull of the moon had a significant effect on changing the Earth's atmosphere.(8) Some Americans argued that a series of recent earthquakes (including the 1811-12 New Madrid earthquakes) had "created an equilibrium of fluid between the surface and the atmosphere," preventing heat-giving lightning.(9)

My absolute favorite theory was also based on the idea that lightning bolts were an important source of heat for the Earth. The cold weather, this theory alleged, was caused by Benjamin Franklin's short-sighted invention of the lightning rod, which by absorbing lightning bolts had prevented them from hitting the ground and heating the planet.(10)

Even people with direct, firsthand knowledge of the eruption at Mount Tambora didn't connect the dots. Much of what we know about the eruption comes from the account of a British colonial officer named Stamford Raffles, who heard the tremendous sound of the eruption from modern-day Jakarta, 240 miles away from the volcano, and observed the tremendous amount of ash that blotted out the sun and choked the ground. By 1817, he was back in Europe, and observed firsthand the economic devastation caused by the prior year's cold weather; his cousin Thomas, who was traveling with him, wrote:

The only unpleasant circumstance in crossing the Jura, and which bespoke the deep poverty of the people, was the great increase of beggars. They were chiefly children, and their number and their importunity were truly astonishing.(11)

Some observers did get close to the truth. Several American newspaper accounts conspicuously mention the hazy atmosphere that year, such as the editors of D.C.'s Daily National Intelligencer who noted "the whole atmosphere is filled with a thick haze, the inconvenience of which is not diminished by the clouds of impalpable dust which floats in the air." These accounts didn't connect the haze with volcanism — and indeed the haze may have been caused by forest fires and dust storms rather than Tambora — but people did identify that haze in the sky could intercept the sun's rays and cool the planet.(12)

Decades earlier, none other than Franklin, when he wasn't trying to destroy the climate by intercepting heat-giving lightning, had put his finger on the solution in the cool years of the 1780s (which caused their own crop failures and thus were possibly partly responsible for the French Revolution, but that's another story). In 1783, he wrote:

During several of the summer months of the year 1783, when the effect of the sun's rays to heat the earth in these northern regions should have been greater, there existed a constant fog over all Europe, and great part of North America... Of course, their summer effect in heating the earth was exceedingly diminished. Hence the surface was early frozen; Hence the first snows remained on it unmelted, and received continual additions. Hence the air was more chilled, and the winds more severely cold.

... The cause of this universal fog is not yet ascertained. Whether it was adventitious to this earth, and merely a smoke, proceeding from the consumption by fire of some of those great burning balls or globes which we happen to meet with in our rapid course round the fun, and which are sometimes seen to kindle and be destroyed in passing our atmosphere, and whose smoke might be attracted and retained by our earth; or whether it was the vast quantity of smoke, long continuing to issue during the summer from Hecla in Iceland, and that other volcano which arose out of the sea near that island, which smoke might be spread by various winds, over the northern part of the world, is yet uncertain.(13)

But Franklin was long dead by 1816, and his hypothesis does not seem to have re-circulated at the time.

Instead, we need to look to the French writer and traveler Constantin François de Chassebœuf, the Comte de Volney, who writers Jean-Baptiste Fressoz and Fabien Locher identify as the only person they've discovered to have correctly identified the cause of the Year Without A Summer.

Volney had a couple of advantages: he was a scholar who had thought seriously about climate during an earlier trip to America, and he was an orientalist who probably subscribed to L'Asiatic Journal, which published an account of the Tambora eruption. In early 1818, Volney published an article explicitly connecting the Year Without A Summer to Tambora, and offering a mechanism for how a volcano in Southeast Asia could affect the weather on the other side of the world: Volney compared the atmosphere to a river, where the famous trade winds were analogous to oceanic currents. He proposed establishing a network of meteorological observatories to report on these air currents.(14)

I unfortunately can't tell you exactly how Volney's theory was received at the time, but it doesn't appear to have made a big splash. The Year Without A Summer did spur new discoveries that would make it easier to interpret future climactic events: Against existing theories that the earth was cooling down, or that climate was immutable, Swiss engineer Ignaz Venetz studied ice accumulations in the Alps and concluded that glaciers had taken up much more space in the past — the first argument for what would soon be known as the "Ice Age."(15) But decades later in 1883, when another Indonesian volcanic eruption affected the world's climate, scholars at the Royal Society who were "assiduous in cataloguing the sound and light shows put out by Krakatoa, never bothered to consider the idea that the world might be cooled down by all the particles in the upper air." The society's editors published a collection of barometric pressure data, but not temperature. It wasn't until 1913 that a systematic study of Krakatoa's eruption found it had contributed to a worldwide drop in temperature.(16)