"it seemed to ring like a dulcimer on the frozen air"
This refers to the hammered dulcimer, a stringed musical instrument.  The strings are stretched over a sounding board and then struck with two small hammers.  Variations of the instrument have been used in dozens of countries, in different continents.  The word 'dulcimer' is from both the Latin word 'dulcis', meaning 'sweet', and the Greek work 'melos', meaning 'song'.  This forms the word 'sweet-song'. 

Listen to a madrigal played on the dulcimer.