It's a tradeoff between fuel power and temp desired. If you're kinda' starved for power (e.g. electric smokers running on 120V/15A circuits certainly fall in this category) insulation is critical to get to even 200F temps in chilly weather.
On the other hand, if you have a big firebox and plenty of wood, simpler-is-better is not a bad mantra.
And then there are pellet grills that use forced convection instead of natural (draft) convection to cook...for those, most of your heat is going out the exhaust so even perfect wall insulation doesn't gain you much. Instead you should slow down your fans (my preferred approach) or add baffling/resistance (e.g. "downdrafts") if you just can't feed enough pellets to keep up with the cold weather.
Your pizza oven is beautiful. I think a similar looking smoker next to it is a grand idea. However not all insulation has the same thermal mass. Bricks take a LOT of energy to heat up. Even with a big fire (and plenteous, cheap wood) that takes time to get to temperature. Corrugated cardboard has negligible thermal mass, while being an excellent insulator, but it's usable temperature is considerably less than Fahrenheit 451, regardless of what the book says. I'd suggest starting with a steel body (esp. if you can weld) cover it with Hardee-board type insulation, then foam board (of course you'll need some steel structure that protrudes through the foam underneath to carry the weight load) and then cover the foam with brick like your pizza oven. That will give insulation without needing many hours to reach a usable smoke temperature, and will be a nice visual complement to your pizza oven.
So what sort of smoker build/technology are you leaning towards???