In most pellet machines (well, all, unless you mod them or count the electric igniter) the heat all comes from the wood. The temp is controlled by adding fuel more often and by running more air through the pellet crucible to burn that fuel quicker. As such, you have a several-minute response time that your control system has to deal with. If your outside temp variation is on a timescale of that heating response time (e.g. direct sunlight that goes in and out of a cloudbank) the controller is going to struggle keeping the temp constant. But for slow changes (e.g. early morning chill to mid-day heat) your controller shouldn't be affected by the external temp change. Yes, you'll burn more fuel when it's cold, but that's true whether your fuel is pellets, splits or utility electricity. Blankets and boxes that better insulate the cook chamber reduce your fuel use, but it's not dramatic because most of your heat loss is out your chimney/exhaust, not out the walls. This is because pellet machines use an externally powered fan to variably provide oxygen to your burn pot. Even at its slowest speed, it's moving air a lot faster than what natural convection and draft would cause, so the fraction of heat going out the stack relative to that going into the walls is greater than just about any other smoker technology.
The steel wall thickness has a negligible effect in reducing the heat out the walls...metals just have too much thermal conductivity. You need to use other materials, esp those with loosely-layered structures like blankets and cardboard for that sort of help. However, thicker walls take slighly longer to reach "operating temperature" upon start-up. However pellet grills heat up fast (compared to other technologies) so that's not a problem. Thicker walls also slightly reduce temperature variations, again from the "thermal mass" argument, but it's a small effect. Plus, thicker walls take longer to corrode/rust through so they last longer, although that sounds like a financial argument and I think money-wise you're always better going with a cheap unit that you just replace more often.