You'll need boots, a warm jacket and a hat and gloves, but you won't have to dress for an expidition to the North Pole. In October and November you get long twilights AND the added bonus of the Aurora Borealis . But think about it - in the off season you'll see a new face of Iceland and save money too. Airfares are slashed to half their summer highs. Hotels are cheaper.
Nightlife is hotter.
The tourist crowd is gone and there is still lots to see and do. Many Icelandic bus tour operators will take you out into the depths of the countryside well into October . There are off season Jeeptreks and ski and hiking tours as well. You just have to change with it and be open to new possibilities. Icelanders operate this way and you can too.