I'd like to upvote this question, but there isn't really anything to answer and as phrased it's very broad. "Yes", pretty much sums it up. The cold would cause a mass extinction. Survivors of that event would then colonize the equivalent niches either by temperate plants moving south or tropical plants that did survive adapting (or more likely a mixture of both those things). That's basically what always happens. —
Tim B ♦ 5 mins ago