Just b/c AC is broken, does that mean heating is also broken in an HVAC system?

When the AC went out at the end of May, we were told it ran out of R22 due to a leak; this, in turn, caused the compressor to burn out. When cold weather comes, does that mean the heat pump won't work either? What about the furnace? (I recall the realtor mentioning we have both heat pump & furnace back-up.)
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