This is a good question. I would say that the 19th century was actually a very important time for Mormonism, because it was the foundation of Mormonism through the religious experience of Joseph Smith. The Mormons also reached Salt Lake City in 1847. However, when it comes to the the impact of Mormonism to the broader society, I would say that it was very minimal.
There were so many other important things going on in the 19th century in America. For example, the industrial revolution was in full swing. This was a much bigger event than Mormonism. Through the industrial revolution, America became a greater nation. There was also the issue of slavery, which American faced. Then there was the the civil war, which nearly rent America apart from 1861-1865, and the assassination of president Lincoln. All of these events are much bigger than Mormonism.
Fun Fact: In Polynesia, religion is a passtime, and an option. Mormonism says it teaches the older versions of faith in the islands. However, in the islands Mormonism, in order to stay, had to convert their own gospels to fit the cultures of the islanders.