Is the burning smell that comes through your ducted heating vents dangerous?

Depending on the amount of dust accumilation. It is normal for the first run after the off season ( even cleaned or new elements ) to emmit a " burn off " . However proir to placing an existing electric heater into winter service , proper maint. of the unit is highly advised.

I hope this answers your question , Tom H. HVAC proffesional, New Orleans area