PLYMOUTH, Wis. — It’s a common observation here that you can’t turn off the cows — not for Christmas, and not for a trade war.

So as President Trump’s aggressive trade measures prompt other countries to retaliate with barriers to American goods, dairy farmers and cheesemakers in the rolling, bright green hills of Wisconsin are growing anxious about what will happen to all of the milk and cheese they churn out and typically sell overseas.

“If export markets get shut off, I could see us getting to the point where we’re dumping our milk in the fields,” said Jeff Schwager, the president of Sartori Company, which has produced cheese in a nearby town for generations with milk it purchases from more than 100 dairy farms throughout Wisconsin. “It’ll be a big ripple effect through the state.”

The president’s trade approach stems from his campaign promise to revive American industry, particularly manufacturing, by putting “America First.” That promise helped propel Mr. Trump into office. But the ramifications of the president’s protectionist approach are beginning to be felt in the towns and counties that elected him, as the downsides become more evident than any upside.