You could try to insulate it more by adding to the outer shell with double foil-backed sheet, and possibly increase your BTU output with an additional heater element mod (which, if your not careful will void the warranty). Be sure to protect from the wind and precipitation as much as possible...that's a biggy for killing smoker temps. Growing up in S/W North Dakota, I can tell you that your -20* C/-4*F is a mild winter's day. We used to get -30* F days/-40*F nights for about 6 weeks beginning in late December.
I understand your wishes to have a set & forget smoker, but electric heated just may not get it done in the winter in Canada. I don't recall how many watts the heater element is in the Bradley, but it seems to me that they're a bit on the lighter side, relying mostly on insulation to hold what they can build for heat...it just doesn't work well in colder climates, unfortunately. If it were around the 1,200-1,500 watt range, you'd stand a lot better chance for success in cold weather. Also, try methods which reduce the need for smoke chamber cabinet door openings...sometimes it's not easy, but the less time the door is open the better off you'll be. If the smoker is taking more than 30 minutes to get up to stable temp, it probably won't hold that temp if ambient conditions turn for the worse, and it will probably struggle for hours to get back to temp if you throw a full load of cold meat into it.
I have propane rigs for cold weather smoking, and I wouldn't have it any other way. They do need to be checked periodically, but once you get the temp dialed in, if ambient conditions don't change, neither will chamber temps. You can pretty much tell as afternoon temps drop that you'll need to bump the burner valve a crack, and then again about 4 hours later, and back it off in the morning (on all-night smokes such as beef brisket or pork butt/picnic). Any decent propane smoker (and most cheapo's) will get you well above low & slow smoking temps in mid-winter without even breaking a sweat. My Smoke Vault 24 can usually push about 350*F above ambient (sometimes closer to 400*F), and my old 3405-GW GOSM can get pretty close to that as well. Mid-summer I can crank them to around 450*F for cleaning/seasoning if I want to. I've had -30F winter nights here in recent years, and was still able to push a 225-250*F smoke chamber temp and had more dial to go on the burner, so it didn't even worry me that I'd have trouble holding temps hot enough for large beef or pork cuts.
For more stable temps in a propane smoker, I use pea gravel in the water pan instead of water, and a foil liner on the gravel to catch drippings so my gravel stays clean...works like a charm. If I want a bit of added humidity at the start of the smoke for improved smoke reaction, I just add a bit of water to the foil liner and let it slowly evaporate...1 quart will last for hours depending on my set-up and which smoker I'm running. I started doing that in a charcoal vertical smoker last spring and loved the results so much that I now run all my vertical smokers that way.
Anyway, for the money (much less cost than most every electric smoker, barring the ECBs) propane smokers have a lot to offer in versatility and cold weather performance...I like to cook with charcoal, but sometimes I just need a break from tending the fire, or I need a little more umph when mother nature is on the prowl...propane gives me both.
If you're considering insulation, you may want to browse through the electric, propane and charcoal smoker forums to get some ideas what others are doing, but I'm betting the electric forums is where you'll find the most. I've never considered insulating any of mine, otherwise I'd know a few good threads to direct you to.