Will audio gear be ok in unheated house

Marine supply stores offer low wattage heater sticks expressly for dehumidification. They're not expensive and far safer than a room heater or light bulb. I'd also consider making the closet more theft-resitant with a heavy duty door, hinges, and lock. At a minimum, line the inside of the door with 3/4" plywood and install a deadbolt. It won't stop a determined thief, but it will slow and hopefully discourage them. Look

@glennewdick ....with some simple insulation and a fresh bulb, your concept ought to fly nicely....the only fly in that soup would be an extended power outage....but with desiccant.in that space as well, ought to be as safe and sound as possible..👍.

@dill

"when I leave in the fall for theft worries"

- So you are changing your mind about this reason?

Your quote left off most of the original sentence.

It said:

when I leave in the fall for theft worries, but mostly because I am not sure the equipment will be OK in an unheated house in an often damp environment until the late spring when I return.

Theft worries are not the primary reason for moving the equipment.

I let my equipment, including tubes, get down to around 55 degrees fahrenheit in the colder months of the mid-lower South. If in the higher North, I'm not sure I would trust in house temps in the 20s. Friends have a camp in Adirondacks that is closed for the winters. I'm sure the inside temps get into the low 20s but they only have some basic TVs that can be replaced cheaply but those have stood up well. 

Do not put your electronics in plastic bags. Those packets can only do so much and then they are done. And moisture over time is very bad.