There were 4 sources of Swedish cavalry
The Royal household cavalry
The "Hovfana" provided the king with a standing force of cavalry which both served in the field and provided a mounted escort during peacetime travels. (The Drabant bodyguards were too few to provide proper security on the road and were not trained in the use of the lance or crossbow/arquebus)The Hovfana was 200-300 strong and was at first armoured lancers with a small number of mounted crossbowmen.
Erik XIV greatly expaned the household troops by adding several new units. The "White" made up of lancers and the "Black" made up of Reiter style cavalry. (The colour refered to the colour of their armour) These units were disbanded after Erik lost the civil war in 1568 as they had remained loyal to the end.
Before 1563 the use of the lance is unclear, it seems that the lance was still used at least up to the 1540's and instructions issued durint the war with Muscovy shows that at least on paper it was in use in the 1550's but how the men really fought is not known.
The lance was not used in combat during the war of 1563-1570, the troops left the lances in storage and fought with pistol, sword and an assortment of warhammers and maces.
A little studied part of the Household cavalry is the Ducal companies, the younger sons of Gustav I were granted various dukedoms and they each raised a company of ducal houshold cavalry. Becaus they were outside royal control we don't have much documentation about them.
The Noble levy
A Swedish noblemans status and priviliges depended on his providing the Crown with armed service. In theory failure to do so would result in being stripped of noble rank, in practice this was seldom done. Erik XIV was the only one who strongly enforced that rule and he ended up with a revolt and civil war that cost him his crown.
Based on ones income and wealth you had to provide a certain number of armed horsemen, the poorest gentry would serve in person while the great magnates were to supply small bands of well armed retainers. The early muster rolls from 1529 show that few men served in full armour, most were mounted crossbowmen in half armour who could use short lance in addition to the crossbow. But by the later 1530's this had changed and the majority of the noble levy was armoured lancers with only 20-25% of the men serving as mounted crossbowmen.
Pistols began to be added to the equipment in the 1540's and like the Houshold cavalry the lances were not used in the 1563-1570 war with Denmark.
Armed service was expensive and therefore unpopular with the nobility who frequently argued with the Crown about the regulations for armed service. Gustav I walked a middle road and used a stick and carrot approach to get a decent force but not enforcing the full extent of the law.
Erik XIV demanded that the nobility fullfill all of their obligations which resulted in a 50% increase in the number of cavalry raised by the nobility, several hundred families unable or unwilling to provide armed service found themselves stripped of noble rank. The end result was that the nobility rallied around Eriks younger brothers when they revolted against the King in 1568.
Johan III who usurped the throne greatly reduced the armed service demanded from the nobilty, in practice the Swedish noble levy was allowed to go unmustered and unused until the final years of the 16th Century and their military value declined accordingly. Only the nobility of Finland continued to see active service as Sweden became involved in a 25-year war with Muscovy over the possesion of current day Estonia and northern Livonia.
The Regulars
The Dacke Feud of 1542-1543 had showed that the Houshold cavalry and Noble levy were too few in numbers to be able to fight on several fronts. As a result the army reform of 1544 saw Gustav I begin to raise companies of regular cavalry recruited from volunteers.
At first they served as mounted crossbowmen but despite their cost pistols and wheellock arquebus began to spread to these units as well. New research seems to suggest that the spread of firearms was not as rapid as older sources have suggested and despite Erik XIV turning the regulars into copies of the German Reiters & Pferdschützen on paper units still made surprisnlgy large use of crossbows in 1564 during the war with Denmark.
But firearms won out in the end and the regular Swedish cavalry rode to battle with a mix of pistols & wheellock arquebus in the last decades of the 16th C.
The armour worn is not easy to determine, it seems that a form of half armour was supposed to have been worn in the same style that was used by the mounted crossbowmen of the household cavalry and noble levy. For the 1560's whe have better documentation and it is clear that German style "Trabharnisch" were supposed to be worn. Most men would probably have worn only the simplest form with helmet, breast & backplates and mail sleeves. This simple form of armour continued to be used in the war with Muscovy 1570-1595 but the Swedish cavalry became increasingly unarmoured and at one point some units were issued with infantry armours to given them some protection. But in the end armour seems to have almost completly disappeared since it was not precived to been needed. This would cause a lot of problems when fighting the Poles in the early 17th Century