For a one off trip your mum is right, just man up. You can always tell your grand children in 50 years time how the Police pulled over a snowman going to a party on a motorbike.
But for regular trips a heated jacket is the dogs danglies. Did Stranraer to Portsmoouth on a cold February day. About 5 tank fulls of fuel for the Firestorm. However, the heated jacket was the life saver keeping core body temperature warm. Only needed half heat as full heat was too much after half an hour of riding.
http://www.webbikeworld.com/r3/heated-vest/
Only problem is it doesn't fit any more due to gaining a few kgs