When making a trip to Iceland, it is hard not to pay special attention to the country's namesake—namely, its 4,500 square miles of glacier. Ice climbing on the glaciers is practiced year-round and takes place mainly on the Sólheimajökull and Svínafellsjökull glaciers in the south of Iceland, to which day trips are offered from Reykjavík (and Skaftafell).
Hiking trips are also available onto the Snæfellsjökull glacier in the west and the Vatnajökull glacier in the east. Without exception, glacier walking or climbing should not be done without the accompaniment of a trained guide. Glacier walking tours can often be combined with other tours such as jeep safaris and boating on a glacier lagoon. https://www.inspiredbyiceland.com/things-to-do/activities/ice-climbing/