The origination of the term break the ice dates back to old trade practices that involve, well, breaking the ice. When cargo ships became icebound for weeks at a time due to bitter, frozen winters, smaller ships were sent out to break the ice in order to make a path that would enable future trade.
In other words, if you (as a boatman) wanted to get down to business - you had to break the ice.
LET ME ASK YOU THIS...
How do you break the ice with someone you've just met?
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Author/Speaker/That guy with the nametag