Sweden acquired its first laws regarding owning and keeping arms as a private citizen in 1927.

Swedish peasants had by the medieval county laws a requirement to own and train with arms and armour, and maintained that tradition long past when it was abolished de facto with the Alnsö law 1280 and de jure with the first national law of Magnus Eriksson that was introduced in the 1350s. During the waning years of the Kalmar Union, the Swedish peasant militias were well-equipped with arms and armour and often quite experienced through the regular spasm of warfare that was the last death throes of the Kalmar Union. In fact, for some time they held most of the military power in the country.

The long time of peace after the ascension of Gustav Eriksson (Vasa) as King resulted in a degradation of peasant arms - when Gustav's son Erik XIV considered the option to buy arms and armour from the peasants to reinforce his armies during the Nordic Seven Years' War 1563-1570, his officials found that many of the peasant arms were in ill repair, and those that were not were almost uniformly old and not fit for the modern battlefield.

Hunting remained free on common land (which made up most of the forests) in Sweden, and many peasants kept hunting crossbows and later hunting firearms (arqebuses, muskets and later rifles). The question of wether you owned arms or not in the 18th century came down to if you could afford it, and if you had a use for it, rather than any legal restrictions. Hunting weapons were common, as were tools and weapons of self-defence and maintaining order, and weapons to hunt predators (wolves, wolverines and bears, mostly), which the peasants had a legal requirement to partake in.

Peasants served as tolvmän (literally twelve-men, twelve reliable elected officials that served as jurors and judges at the lowest level of court) and as fjärdingsmän, a part-time proto-police duty that required them to maintain order at events, enforce goverment decisions and escort Bailiffs and other officials at tax collection and other official matters. These men would often use long pole-arm style wooden spiked clubs. These were common enough weapons that many were in service when the last large Swedish peasant rising occured 1743. Here's an image of three weapons captured from the peasants as they were defeated after taking the capital of Stockholm. The center weapon is a typical spiked club often used on the countryside.

Peasants also served as indelta semi-proffessional soldiers in the army, being given their equipment and a croft for them and their family to live on and equipment, including arms, to keep and be ready with.

The peasant rising in 1743 seem to have been pretty badly armed from the start - spiked clubs and the kind of converted farm tools you see on the image I posed above. But as they advanced on Stockholm, they armed themselves by breaking into army and local authorities arms depots and enticing soldiers to join them.

That said, arms were generally expensive, and the countryside in general peaceful - there were little reason beyond hunting and maintaining order fo the peasants to own arms. Barrel smithing was a specialised task that required a lot of skill that was rare outside state arms manufacturies that supplied the army. If you wanted more finely crafted arms, you often had to order them from abroad, where there was a larger market in self-defence weapons (pistols) and fine hunting arms from nobility that travelled and held exclusive hunting rights.

But if you had the money and decided you wanted to own arms, there were no laws or bans that prevented you from purchasing and owning weapons. It was still rare since most peasants preferred to invest the money in tools, animals or save up for a failed harvest instead.

One needs to remember that the American farmers, who often owned their own land and did not pay a land rent (tax) for their land often had far more resources than the regular European peasant and thus were far more able to afford to own arms.