Yes and no.

Ice harvesting had been going on since before the Roman period, however it was still a seasonal activity, you could only get the ice in the winter and use it over the rest of the year, using ice houses. If you were rich your estate would have one and over the 19th century home delivery became common. So while it's possible that you had access to ice I'm not sure if you'd had drunk it.

Ice was expensive and almost impossible to get in hot climates until 1806 when Frederic Tudor started shipping ice to the Caribbean by boat so iced drinks were rare until that point (if you've got the ice you want to be warm instead). You example of iced tea didn't get popular until th 1860's. Ice was mainly used for keeping food chilled.

Hope that helps