Cavalry wasn't particularly common in medieval Scandinavia before the 12th century. In 1134, there was a struggle over the throne of Denmark between King Niels, with his son, and Eric Emune, the illegitimate son of Niels' brother the previous king Eric I.
Eric used German cavalry and crushed his uncle's larger forces at the battle of Fotevik. And soon after he became King Eric II of Denmark.
After Fotevik cavalry in warfare became far more common in both Denmark and Sweden (word spreads). It didn't particularly catch on in Norway, which was much more densely forested so not ideally suited to cavalry charges. They relied heavily on mercenaries (but that was increasingly common through out the Middle Ages in this time if you count "mercenary" as paid soldier not in direct service to a lord.) But also had some of the wealthier farmers equip themselves.
This lead to seeking direct cash levies from the communities to fund cavalry. That wasn't unheard of before but generally tribute had usually come in the form of direct military service prior to this.
I have to agree with most of the facts @PlinytheHipster stated, but he does suffer from a severe case of very weird geography. Sweden has twice the percentage of of forested land that Norway does - in relative terms, that number would be even higher in absolutes.
The first clear evidence of the continental heavy knights in Sweden is the ordinance of Alsnö, from 1280. This is actually after the Norwegian sources shows the institution of such an organization. In any case, the professional full-time soldiers of all the Scandinavian kingdoms past 1280 consisted entirely European knights, just like the rest of Europe.
In Sweden, the knights were not paid, nor granted any land at all, only exempt from all taxation. That was an attractive proposal for the richer yeomen, who together with old poorer nobility formed a new low, knightly, class. The old rich families intermarried and consolidated to form an upper nobility who fully adopted the continental ideals of chivalry.
The most interesting part is how the Swedes mastered their forests and created guerrilla tactics specifically to fight mounted knights. First some background though. The centralized Kalmar union insisted on, and could enforce, a heavy taxation of the people. A smaller population thus had to pay more than before the black death had devastated the world. The Swedes wouldn't have any of it. And that's how the Kalmar union broke down in a century of civil war.
In the battle at Haraker in 1464, the Swedish militia ambushed the Danish force as it passed through the forest and won a great victory. They had prepared by felling trees along the road and created several layers of barricades. Some of the people were stationed on the barricades. Others were armed with bows and crossbow and were positioned within the forest along the flanks together with some guns.
After the Danes arrived, they captured the first barricades, but were forced to dismount. They were then met with a fierce storm of arrows from their flanks and took heavy losses before they retreated.