The first thing that needs to be understood here is that from about 1300s to 1809, Finland was for all intents and purposes an eastern province of Sweden. While the common folk was somewhat distinct in that people in Finland spoke Finnish (although folks on the western coast facing Sweden often adopted Swedish and use it still), there was little distinction between "Finnish" and "Swedish" nobility: both were servants of the Swedish king, spoke Swedish (even though some spoke Finnish, too), and generally considered themselves to be Swedish. However, Finnish "nobles" were usually born in Finland, and generally held some idea of belonging to a distinct "nation" or "tribe" compared to the Swedes and others (e.g. Germans) who the Swedish king had rewarded with lands in Finland.

I put the "nobles" in quotation marks because in reality there was very little actual "high" nobility in the Swedish realm during much of the period, and they were even rarer in the eastern provinces. The largest caste of what might be called "nobles" in a sense that they were exempt from taxes and had an obligation to serve were men-at-arms or "knights" (rälssimiehet): from 1345, any smallholder who could afford weapons, armour and a horse and serve the King would gain tax exemption for himself and his possible tenants. The concise encyclopedia of Finnish history [1] notes (p. 88) that the Finnish "knights" held some notion of "Finnishness," which resulted them to e.g. support a domestic candidate in a 1386 election for a chief magistrate. However, this is best understood as a desire to have one's "own man" in a position, not as any indication for actual independence movement: two decades earlier, in 1362, newly elected king Haakon produced a declaration stating that in future elections, a Finnish delegation was to be added to the list of electors "given Eastland's [Finland] demonstrated loyalty and love to the Crown".

Nationality as an idea tied to language emerged only after 1700s, and particularly after the American and French revolutions. Simultaneously, from 1780s, the Swedish crown had run into problems, largely caused by several bad harvests in a row but exacerbated by perceived insensibilities and profligacy of reigning king Gustav III. From about 1770s, he had been interested about conquering Norway from Denmark; however, that would have required Russia to stay neutral. As a result, there were rumors that Gustav would trade Finland for Norway, and this is where the first "real" independence movements are recorded: among the officers serving at the grand sea fortress of Sveaborg [Suomenlinna] just outside Helsinki, there was a secret Valhalla society that at least discussed whether Finland could be independent. Many other officers, notably G. M. Sprengtporten, expressed similar views; Sprengtporten, who had entered foreign service (fairly common at the time) but felt slighted by the King as the latter had "agreed too easily" to Sprengtporten's request for permission to serve under foreign flag (p. 321), eventually entered the Russian service in 1786 and produced a memorandum for empress Catharina II where he proposed an independent constitution for Finland.

The only real rebellion-of-sorts against the Swedish crown resulted two years later, after Gustav III had engineered a war against Russia, at the time embroiled with a war with the Turks as well. The 1772 constitution forbade wars of aggression, so the king forged intelligence reports and planned a provocation that would implicate the Russians. He got his war, but particularly in Finland, the morale was low, and the king's poor leadership exacerbated the affairs. When the Finnish officers realized that they had been duped into a war of aggression and after some serious defeats on the field, they in effect mutinied and pleaded for peace with Russian empress Catharine II. The officers, forming a so-called "Anjala league", still swore loyalty to the Swedish crown and most of them had no real designs for independent Finland, but this was still a serious mutiny. The coming of winter and the end of the campaigning season also ended the rebellion, and some members were tried in a courts martial afterwards, with one being executed for treason.

In 1809, another disastrous war resulted to Finland being irrevocably lost to the Swedish and being conquered by the Russians. Anxious to gain support of the local elite and somewhat of a reformer himself, Czar Alexander I promised Finland a special status as his personal, autonomous Grand Duchy with separate laws and privileges from the rest of the Russian Empire: in fact, Russian subjects did not have any special rights in Finland other than those accorded to all other foreigners. This started a process whereby Finland became in practice autonomous nation, with only foreign policy and defence conducted by the Russian court. According to Finnish position, the Finnish nation had swore fealty to the Czar personally, who in turn had promised to uphold the traditional laws and privileges of the Finns.

The fragmented independence movement was thus appeased, and there were no serious threats to the Russian rule for nearly a century. The Russians actually encouraged nationalistic thinking, particularly the use of Finnish language, to some extent, as this was seen to provide a bulwark against "Swedish influence" so easily seeping from across the Bothnian Bay. In around 1848, there were some student-led movements pronouncing Russia as the oppressor of Finland, but these went nowhere: compared to Western Europe, such social movements found little purchase in Finland at the time.

By this time, the torch of the independence movements had passed from the scarce nobility to students and intellectuals. More and more, nobility was achieved through administrative service to the Russian crown, and these nobles were generally loyal to the Czar. When the Finnish independence movement really started in 1890s, after "Russification" reforms, few if any nobles attended from the outset. So, in a sense, and aside from the brief and inconclusive Anjala rebellion, it might be said that Finnish nobles never really got together in any nationalistic fervor nor did they rebel against the "lawful" ruler.

EDIT: Key source [1] is the aforementioned concise encyclopedia of Finnish history, Suomen historian pikkujättiläinen (Zetterberg et al. , 1987).