If the battery was dead and the alternator wasnt charging enough your car might run a bit rough but it should not effect performance.
You had a tune (plugs,boots) up latly?
Also some fuel injection cleanr ran through regularly helps keep the fuel system clean, so it can function at 100%.
The stock alter is only 105 amps. They sell them up to 140amps.
Since you liv in the arctic

might consider a dry cell battery such as the yello, red tops.
they are expensive, but the dry cell is more stable at colder conditions and should last much longer.
Dimming lights are pretty commen.
Just last night I was behind an 06' Corvett, he was listening to "Jan & Dean" (

) and every beat his tail lights would dimm. Thats not right!