For some reason, Iceland is not very well known for their ski areas. But this is totally unfair in my opinion.

The ski area above Akureyri for example, is a great place to visit. It is only a 5 minute drive from town and from there you have a beautiful view over Akureyri and Eyjafjörður. The ski area is not very big, but you can definitely enjoy yourself for a few hours / a few days there. If you visit during the week, there's a big chance you'll have the slope almost to yourself because most Icelanders will visit during the weekends.

You can get a ski pass for a few hours or a few days. And of course you can also rent all the equipment on site.

Make sure to check the website before you go, because the weather can of course be a bit unpredictable in Iceland, so the area might be closed in case of bad weather.