We do not support demos of Icelandic Horses riding on ice, either on rivers, lakes, rinks, or arenas. It is too dangerous, and may be detrimental to the horse's long-term soundness.
If a child tries this, we may lose the child and the horse.
Think about it. Just because it may be done in Iceland, does not mean it is right, or good.
Pounding the horse's metal shod foot against the hard ice must be uncomfortable, if not painful to the horse. Additionally, there is the problem of the ice nails grabbing the surface and interfering with the normal action of the foot to slide into place, and putting torque onto the hocks.
Horses like to play games with people. Like kids who enjoy spending special time with Mom or Dad, horses also enjoy engaging with people. It adds to the relationship, and makes a smarter horse, one more willing to have two-way communication.
Icelandic Horses (aka cheval islandais, island hast, islandske hest, island pferde, islenskir hestar, ijslands paard, islanninhevonen, islenskihesturinn, islandisches pferd, hestur, islandpony, icelandic pony) really seem to enjoy interacting with humans in ground work, games, toys, clicker training, or anything in a positive, relaxed learning atmosphere.