Despite a terrible war raging for four years, immigration into the Union increased throughout the war.

Congress and Lincoln passed laws which encouraged immigration. The Northern States had wanted to do that for years prior to the war but had always been blocked by Southerners as they wanted to limit cheap immigrant labor and thus preserve their high slave prices.

The Immigration and Homestead acts were passed, making it easy to immigrate and to get free land out West as well.

Near the end of the war, Lincoln spoke in front of Congress at the State of the Nation and spoke about how much the population of the North was increasing and the GDP was increasing through the war. In contrast everyone knew the Southern states was having a population decrease due to battlefield deaths and their slave based economy was being wiped out. The picture from that speech was that Irregardless of particular war battles, the North would eventually win just by out growing the South.

I believe the total number of immigrants was around 3 million people. I'm sure the bureau of statistics would have an exact number.

In regards to what the immigrants thought about the war, I'd say there were a few major opinions. 1) most who immigrated probably did so assuming they would not be directly affected. To most people, the war just kept going longer and longer and more and more bloody. 2) in NYC when the draft list was called out with mostly Irish names, those recent immigrants were outraged at being targeted and rioted. 3) a massive number of immigrants joined the Union cause and fought and died for their new country. In particular, Germans were highly educated and hated slavery and were quick to volunteer. I don't know the precise count but would suppose a couple hundred thousand Union soldiers were born abroad