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Well, I suppose it depends on what kind of equipment you are keeping in the shed. I did some general searching for some common transistors and linear IC's and they're all rated for storaqe temperatures upto -65 C. Some are -55 C etc. Most electrolytic capacitors are rated for -40 C.
Of course, if you have sensitive instruments and such, I would find a warmer place to keep them.
Also, if you're building circuits and such out in -20 C temperatures, you may experience a higher range of fluctuation for values of capacitors, resistors and such.
Another topic to think about is the fluctuation of temperatures between night and day. I imagine the broad difference between temperatures at night, and temperatures during the day will put more "strain" on the components. Of course, this type of strain would take years to show any effect on the component, but the possibility is there.
Finally, I think you'll be okay with storing things out in the shed, but there may be some long term effects that may take a toll on your equipment.
You'll be fine as long as you dont try to actually do anything. Lets assume youve moved out there and been working with no trouble. You pack up for the day and the temperature drops. The moisture in the air will condense on everything then freeze. In the morning you will switch stuff on, and as the scope warms up past freezing the eht will flash over and blow out the input amplifiers. Multimeters will for several hours divide the thing to be measured between the 10meg input impedance and the damp board. Everything will sizzle, spit, hum and tell fibs. And the surviving kit will just start to make sense and its bedtime.
I've had a couple of shops "outdoors" and the only real problems I have had are waiting for the test equipment to warm up (scopes, signal generators, vtvm, beer warmer) also, circuits that you build other than simple DC ones can exhibit quite a bit of variation in performance over -20c to normal room temp. Soldering takes longer, breathing on parts can cause condensation. I never did have anything electronic that was ruined by the cold though.
Don't know where you are located but frankly I would be more worried about high summer-time temps in a closed up shed.
And speaking of condensation, that only normally occurs if something is cold and is suddenly exposed to warm, moist air. Not likely to happen over the course of a normal day. Sorry to hear about your banishment to the shed :cry: