Oh, and I think the army should be able to march to Jutland, like it did in 1644 and 1658, there's no real need to maintain naval superiority if the army is already on the continent. It helps for supplies and reinforcements, but is not absolutely necessary - Sweden can raise capital in the form of loans and the tolls and tariffs of its German possessions and raise mercenaries from the continent with that.
As for Älvsborg/Göteborg, that it would come under siege and be blockaded by the Danish navy was expected - it has some impressive fortifications, including
Älvsborgs Fästning (both the old and the new) and many other fortifications. Göteborg would hold any siege for a long time before it could be reinforced overland.
The duty of the Swedish navy in this time was;
1. Maintain the supply and shipping routes between Sweden and its Finnish and Baltic possessions (rarely challenged).
2. Maintain the supply and shipping routes between Sweden and its German possessions (often challenged by the Danes).
3. Gain naval supremacy in the southern Baltic.
4. Gain naval supremacy in the western Baltic, directly challenging the Danish navy in its home waters. This would be a mortal threat to Denmark, as then all communications between the Danish islands, Jutland and Scania would be broken and the Swedes would be able to land a navy.
Relieving Göteborg or operating in the North Sea would be very far down the priority list, if present at all. If the Swedish navy tried to cross the Sound, the Danish navy would assume it was trying to do 4. and directly challenge it.
However, all these points are pretty moot, as the Swedish navy did not operate during winter at all. The ships were laid up in mid-November and fitted during April. Depending on the ice situation in the Stockholm archipelago, the navy would be battle ready mid-April to late May.