Will audio gear be ok in unheated house

Don't forget salt air too as a potential issue.  This can be a bigger problem with components that don't have solder mask on the PCB's, or worse, are point to point wired.

I have had a stereo system in my barn for 10 years with no problems.   Yamaha NS 690 speakers & NAD 2400 amp.   Temps would get below freezing a couple times each winter.  And below zero the year we lost electricity.   

I would suggest burying the equipment in the ground at least 9 feet deep.  That will also help against theft.  But don't forget to mark the spot! 

They will be fine. Much to do about nothing. My speakers in my tractor barn out back (South Dakota) look and operate just fine, freezing temps in winter and lovely Black Hills summers. Like tbick I have had the same speakers in the barn for years. I heat it only when out there working in the winter with a Reznor waste oil heater. Old Sf speakers look and sound great running off an old Cyrus Integrated. 

I think the humidity is more damaging than cold. I moved into a stone cottage in rural Limerick, Ireland, and have lost a few pieces of kit. Humidity here averages 75% minimum sometimes reaching into the 90%. Stored for a long time the power caps discharge completely and then draw huge amounts of current at switch on. When I moved country I sold a lot of stuff including my variac which I used to slowly bring equipment up to voltage. 

In future I will do as @puptent suggested, vacuum bag the components but only after leaving them overnight with a dehumidifier running.