I'm in the middle of a snow storm right now and for some reason there is a burning smell coming from the vents. The HVAC unit is electrical and its outside and there isn't any type of cover on it so should I turn the heating system off and get space heaters until I can get an HVAC technician to come service the unit.

If you are in the same storm as I, there's a lot of blowing with the snow. You may have had some insulation get wet. Personally, I would run it unless you fear it may catch fire.