Is it a sign of something if my daughter likes the taste of metal?

Doctor can evaluate: Everybody puts out sweat and oils onto their skin. Sweat has salt & ammonia (like urine does), plus some other chemicals. Chemicals on the skin will react to metals & metallic compounds. Metals are everywhere: jewelry, doorknobs, spoons, bikes, nails, chains, playgrounds, etc... Metallic compounds may be in: cosmetics, soaps, lotions, antiperspirants, shampoo, etc... A doctor can evaluate further.

Possibly: Talk with your pediatrician. This could be what we call pica, get routine bloodwork to check for iron deficiency. The other danger is that if she accidentally ingests a metal object which could lead to a while host of other problems.