art style?

Church's style was a blend of Romanticism and factual naturalism, meaning his works display both a "scientific eye" and Romantic elements learned from his teacher, Thomas Cole, who's paintings typically incorporated some moralizing theme. There's an interesting article I found about Church and Romanticism if you're interested:
http://www.haberarts.com/fchurch.htm

If you need anymore info on Church, check out any American Art textbook. He'll be in there.

Art style means if the piece is abstract, realism , landscape, impressionism, abstract expressionism, baroque and so on.

He's a landscape painter.

I guess his style would be realism. The style of art means what the category the piece falls under, or what kind of techniques are used by the artist. It can also be what kinds of subjects are in the piece.

I would probably call the style any of Frederic Church's paintings "realism" or "romantic realism". The Hudson River school of painters tended to find a glorious piece of nature and glorify it even further. They dealt primarily with the natural wonders of the North American continent.

"Style" in painting usually refers to categories. The "isms", basically---realism, impressionism, expressionism, cubism, etc. It can also refer to a technique, i.e. "the artist's style is loose and painterly."