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Why Stay?
If they have a good supply of food, there's no reason—no matter the temperature—for robins to go anywhere until their food is gone. Robins that don't migrate as far gain advantages. They don't use energy in long migratory flights. They're better placed to claim the best territories for spring nesting. That's why some stay!

"This afternoon I saw a group of 13 robins after the ice storm pushed through today—most of them all in one small pear tree."
Melissa M., Lancaster, Pennsylvania (February 5, 2014) 

"We had snow and ice today and a wave of robins was in our crab apple tree. Between all of the ice on the branches, the birds were picking off old fruits."
Holly in Bethlehem, Pennsylvania (February 5, 2014) 

Robert Perron
Robins in snow