If you are on the south coast then I recommend going for a glacier hike with Icelandic Mountains Guides (previously named Arcanum) they also have ice climbing tours. I truly belive no one should leave Iceland without hiking on a glacier!
Icelandic Mountain Guides will take you to explore Solheimjökull all year round!
Use code KYANA10 for 10% off when you book with Icelandic Mountain Guides or Arcanum