The war largely did not affect the New World, although naval battles between colonial powers (Spain, Portugal, and the Dutch) did occur and the Dutch did seize some land in Brazil from Portugal during the course of the longer Eighty Years War between the Dutch and the Spanish that ended with the same treaty as the Thirty Years War. Of note there is that the Portuguese crown was held in personal union by the Spanish Habsburgs throughout the TYW.

Besides the Dutch and the French (who joined the fray late), most of the powers opposing the Habsburgs Emperor simply did not have colonial holdings outside of Europe. England had some brief formal involvement and substantial informal involvement through volunteer forces, but most of the island kingdom's New World colonies were still very unsettled (the Mayflower having only left in 1620, for instance) and they largely sat out the war. So the main belligerents against the Emperor for the core of the war were Sweden, Denmark, and most of the Protestant territories within the Holy Roman Empire. Most of the war's fighting occurred in modern-day Germany between the Emperor and these groups.

I'm afraid I can't speak specifically to what New World settlers and indigenous peoples thought about the war, as that's outside my field of study.

My main source here is Peter Wilson's Europe's Tragedy: the Thirty Years War, which is an excellent full history of the entire war including the run-up to the conflict and the effects of the Peace of Westphalia that ended it. I recommend picking it up if you have a lot of interest in the conflict; it's dense reading but very informative and well-written.