Iceland trip

I'm leaving for Iceland on the 20th.
I want to spend most of my time chilling out in nature, bathing in natural Hot Springs, and watching northern lights.
But I also plan on doing a bit of exploration on my own to try to find some ice caves that I could visit for free, without using guided tours.

Two questions came to my mind:
1) How to create makeshift-crampon so that I can do some mild exploration around the glaciers to find some ice caves? (Think of two different scenarios for the available resources: a stranded backpacker, and a cheap crafty urban scavenger.)
2) In case of fluffy snow, how does one end up building a snow shelter? (I believe compacting and waiting works out well, but I must admit I cannot remember... and does it really harden that much when it's only -2°C/29°F outside?)

If you have any other miscellaneous interesting things to share with me about Iceland, it would be appreciated. :)

I don't have much to say but have fun and be careful, I know a fella that went to iceland and came back with a wife.

My daughter went to Sweden last year January 10-18th. They stayed at the Ice hotel. Not only was it actual temps of -20F to -40F each night but there were WINDS. She said there was only about 1/2 hour daylight each day; and even in Stockholm the temps were unbelievable. They road arctic ponies 5 miles on a guided tour to a small camp (in the dark of course since no daylight). She is an experienced horse rider but was deeply concerned her toes were frozen, even tho the hotel provides all the needed gear.

She was born and raised in Milwaukee and Chicago, near the lake with the bitter cold wind chills and actual temps of -20F at least several times each year. So it really is cold. Please be careful. It is not a 'loss' to realize the temps are too hard for you at a certain time.

Buy good crampons.

I might have some in the shed. Don't know if they'd get to you in time.

I've had Iceland on my list for a long time now. I assume you'll be renting your own car to get around? Sounds like an awesome trip, hope you snap some photos!