I think there's a few story lines getting crossed here. I can't speak to the OP comment about North America creating the trend of iced drinks in Europe, but it seems like Frederick Tudor and the resulting ice industry was pretty influential in promoting ice in cocktails, etc.

From New England Historical Society:

>Frederic Tudor expanded his business to Charleston, Savannah and New Orleans, developing new sales techniques along the way.

>He gave bartenders free ice for a year after teaching them how to keep it frozen in a ‘refrigerating jar’ and how to make cocktails like the Smash. He sold ice to Havana coffee shop owners and the keeper of the Tivoli Gardens after teaching them how to make ice cream.

Also:

>Between 1844 and the early 1850s, the remarkably pure ice from Wenham Lake in Massachusetts became a fashionable luxury among the British aristocracy. The best London hotels put up signs advertising Wenham ice. It was said you could read a newspaper through a block of Wenham Lake ice two feet thick.

>Wenham ice inspired the popularity of cocktails like sherry cobblers and mint juleps in London. No fancy dinner party was complete without it, and Queen Victoria insisted on it.

>A competitor to Frederic Tudor, the Wenham Lake Ice Co., had promoted the stuff.