Iceland is in its storm season right now, October to April. Most trips are unaffected, but a storm reroutes flights and closes beaches at a day's notice — the packing consequence is a buffer day and a charged power bank, not different clothes.
Going in September
The open season: long days, passable roads and the mildest weather of the year. Still windy, still wet, still worth a proper shell.
What this means for your bag
Something genuinely windproof
Wind is what makes the cold unbearable here, and an umbrella is useless in it. A hood that closes, and gloves.
See the Weather Protection packA packable rain shell
Not a winter coat — it stays warm through the rain. A light hooded shell that folds into its own pocket ends up in the day bag instead of the hotel room.
See the Weather Protection packLayers, not one thick coat
Three thin layers beat one heavy one: they cover a wider range and pack smaller. A base layer, a fleece and a shell.
See the Winter Warmth Kit pack
Build a packing plan around the season you are actually travelling in.