I have a vertical charcoal smoker with no insulation, and I did a 18lb turkey last week with no problem. I was able to keep the temps in the 235-250 range without much work, even with a classic Nor'Easter moving in, with wind blowing, and temps in the teens. Is keeping temps up that much more difficult with an offset smoker?
Horizontal smoke chambers have much more surface area exposed at the top side, and a side fire box has it's top side exposed to open air also, along with a less efficient means to transfer the heat into the smoke chamber, being side-flow instead of vertical. These situations combined together create an inherently inefficient thermal design. To compensate, much higher BTU output is required from the fire box, and unless a near perfect combination of mods have been done to the typically less expensive models of stock offset smokers, you won't get a hot enough fire to cook with using charcoal or lump. My Brinkmann SNP suffers the exact same problem, but while mine was modded with a full custom tuning plate enabling me to use over 90% of the cooking grate with only 15-20* max grate temp variances, it was a very inefficient design, especially for cold weather.
My Brinkmann Gourmet charcoaler, as heavily modded as it is, has no trouble getting into the 300* range if I so feel inclined, but can do it with far less fuel than my SNP would burn. Yes, there is a huge difference between the two as far as cooking grate surface area (about double for the SNP), but my Gourmet, being a vertical smoker, can run on 0.5-0.75 lbs/hr of briqs in fair weather when the SNP was using 2-3 lbs/hr. I only fired my SNP a couple times in cold weather and thought I'd go broke buying briqs (2-20lb bags for an 18-hr brisket smoke). In sub freezing temps, my Gourmet uses just over 1 lb/hr @ 225* chamber temps, and this is with my intake air dialed in at about 40%.
In terms of fuel use and fuel efficiency, horizontal smoke chamber vs vertical smoke chamber is no contest, IMO, and once a side fire box steps onto the playing field of a horizontal smoker, the point spread gets even bigger. If you can't overcome the inefficiencies in cold weather with a particular fuel source, you either have to go to a hotter burning fuel such as changing from charcoal briquettes to lump, insulating the smoke chamber, or adding a propane burner, which incidentally was my main heat source in my SNP for over a year.