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.