I think he's mistaken. A vehicle with electronic fuel injection will adjust the fuel according to how much air is entering the engine so it makes no difference with fuel economy if the filter is more or less restrictive but a clogged air filter will limit performance. On the older carbureted engines the air filter being restricted would kill fuel economy because fuel was metered with a venturi effect and the restricted air filter would cause the carburetor to pull more fuel into the mix, sort of like having the choke on all the time. A common problem with a K&N filter on a vehicle with a MAF sensor for EFI is the oil from the element can coat the sensor wire and cause a problem with fuel control. When that happens it turns on the check engine light and sets a fuel control trouble code.
That being said the cold weather hurts fuel economy for a number of reasons but I think the biggest part of that is the fact that it takes much longer for an engine to reach operating temperature and go into closed loop. A cold engine needs a richer fuel mixture to run properly and a fuel injected engine uses engine temperature as one of the main inputs for fuel control. The gas you get at the pump is a different blend for cold or warm weather and the gas you get makes a significant difference in fuel economy.