Will audio gear be ok in unheated house

I like the idea from Surfmuz. You can take it to another level by wrapping it in plastic or a garbage bag and putting some desiccant in with the components. You can buy a bunch for under $20. That combined with the process listed above you are set. They can only be used once unless you buy the rechargeable kind. 

Maybe not the same issues, but I used a vacuum cleaner and seal-able bags, sourced from my mother in law, when we put the "stereo" in storage during our big "expedition". I'm pretty sure it got well below freezing in the unit. Everything survived with no damage I could detect. My old cabin Near Breckenridge, CO was broken into several times, BTW, but high transient population...

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!