Tool manufacturer Snap-on says President Donald Trump's visit to the company's headquarters in Wisconsin will highlight "the essential nature of American manufacturing to our nation's future".
Shipments of ultra-filtered milk, which is used in cheese-making, had been duty free until recently, after Canadian milk producers objected.
Andrew Cuomo sent Trump the letter on Tuesday.
The White House confirmed that President Trump is coming to Kenosha on Tuesday. The White House says the program undercuts American workers by bringing in large numbers of cheaper foreign workers, which drives down USA wages.
About 70 dairy producers in both Wisconsin and NY are affected.
The officials say the order will ask federal departments to offer changes so that H-1B visas are awarded to the most-skilled or highest-paid applicants. Regardless of political partisanship, the Snap-on website said "it's always an honor when our contributions to society are recognized - especially by the President of the United States". Gov. Scott Walker is expected to take part in the event, however, House Speaker Paul Ryan is out of the country and will not attend.
The company is located in Ryan's congressional district but Ryan won't be there because he's leading a congressional delegation on an overseas trip this week.