Interesting question. I found an answer for you. Diamonds are called ice because of their thermal conductivity property. When you touch them, they feel cold because they are drawing heat from your body. Most other gems do not have this property. Diamonds conduct heat even more readily than copper. The conductivity is due to the diamond's extremely high strength.

I don't think a complex explanation is needed (though I enjoyed reading it!). A pile of diamonds looks rather like a pile of crushed ice.

I agree with peachy - ice and diamonds both have a glint to them and sparkle. thus the metaphor.

Well, because its brightness and its way to products energy.