That's not true, roots will continue to grow in the winter as long as the soil isn't frozen.
This is a far cry from your first statement of “roots WILL continue to grow as long as the ground is not frozen” if you are repeatedly damaging roots of a tree then this study shows that a tree CAN grow roots even in a state of dormancy. Although 40f is a ways from frozen as well. The ground will not even begin to freeze until temps are 32 f for a period of time.Only took 30 seconds to research this but here's one: https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=20&ved=2ahUKEwjaxPnL6frjAhVSbc0KHWPUCmMQFjATegQICRAC&url=http://arnoldia.arboretum.harvard.edu/pdf/articles/1989-49-4-tree-roots-facts-and-fallacies.pdf&usg=AOvVaw3pAK1jX5_VOCaqpFpCTq8a
"By repeatedly digging up, measuring, and then reburying them, researchers have observed that roots can grow throughout the winter—whenever soil temperatures are above 5 degrees C (40 F) (Hammerle, 1901; Crider, 1928; Ladefoged, 1939)."
I learned it because my old house had issues with tree roots blocking my sewer lines and usually they had to be cleaned out during the winter.
Most studies show that trees do not grow roots while dormant in winter. Including the one you posted and others I’ve read.