If the furnace is resistance electric heat, or if there is a compressor involved (heat pump) the breaker may be too small.
If the furnace uses another fuel (natural gas, oil, LP etc.) and the electricity is needed only for control wiring, the breaker should be sufficient.
The sub panel should have breakers in it too for each of the needs.
All insulated wire has a size on it, either painted on the side of it or etched into the insulation. This print should occour each 2 to 3 feet; use bright light and maybe even a magnifing glass.