The UltraGridRow has a CopyFrom method that should do the trick (documentation).  Here's a test for your scenario:
[Test]
public void CloneRowCellsTest()
{
  UltraGridRow objSource = new UltraGridRow();
  objSource.Cells.Add(new UltraGridCell("Original value for cell 0"));
  objSource.Cells.Add(new UltraGridCell("Original value for cell 1"));
  UltraGridRow objDestination = new UltraGridRow();
  objDestination.CopyFrom(objSource);
  objDestination.Cells[1].Value = "New value for cell 1";
  Assert.AreEqual(objSource.Cells.Count, objDestination.Cells.Count);
  Assert.AreEqual("Original value for cell 0", objDestination.Cells[0].Value);  //Ensure that the value was copied
  Assert.AreEqual("New value for cell 1", objDestination.Cells[1].Value);       //Ensure that the new value was set
  Assert.AreEqual("Original value for cell 1", objSource.Cells[1].Value);       //Ensure that the original was unchanged
}