Northern lights in Iceland tonight

Yes. The island lies at about 63–67° geomagnetic latitude, at the edge of the auroral oval or under it: about Kp 2 brings a glow over most of it, Kp 1 in the north around Akureyri and Mývatn, and roughly Kp 4 puts aurora overhead. On most nights the limit is the cloud, not the Kp.

It changes from night to night. On ten years of ERA5 monthly means every place here is cloudy most of the time — Reykjavík a little less than most — but an average isn't the night you're out: the highlands split the island's weather, so one coast can be clear while another is under cloud. The board above reads tonight's cloud at each place.

From about mid-August to late April the nights get dark enough; from May to early August they are too bright. The ten-year cloud record is on the strip above, month by month — and you also need a low moon: the season sheet lists the dark, moonless weeks.

If you aren't used to winter roads, take a tour from Reykjavík or Akureyri — the tours chase the clearer skies. If you drive, check the roads (umferdin.is) and the weather (vedur.is) first: winter storms close roads, and the south coast's gusts can be dangerous. Never stop on the road for the lights — use a proper parking area.