by any chance do you have 20W50 oil in your bike?
for cold weather you want 10W40 or 10W30. The oil really does get like glue when its below its rated temp range.
Dont look at oil weights vs temp on the internet, look in your owners manual. If you dont have one for your bike you can download it for free from the Yamaha motorsports website.
If your oil is ok for the cold, then the starter clutch is the thing that engages the flywheel. If its not spinning the engine but the starter motor is spinning, the clutch is not working, no matter how it acts when you turn it by hand.