Steve,
Since you have stated that your string was hitting your coat at the chest area, all the posts about cutting down on the bulk around your arm become pretty meaningless, although very well-intentioned. The best way to cut down on bulk but stay warm is to go with something like a PrimaLoft One insulated jacket or vest from companies like Kuiu (Spindrift), Sitka Gear (Kelvin), or Patagonia (Nano Puff), with a more fitted soft shell jacket (i.e., Guide Jacket from Kuiu or Stratus Jacket from Sitka Gear or Element Jacket from Core4Element) over the insulated garment. These keep you warm in most conditions but also keep bulk to a minimum. Of course, use a good base layer, like Merino wool. There is always the potential that the temperatures will drop low enough to make this clothing insufficient to keep you warm, but wearing a pair of Sitka Gear insulated bibs (Incinerator or Fanatic) or pants (Kelvin) will keep the lower parts of your body much warmer, which will allow your upper body to conserve lots more heat. The chest protector might work too, but not unless the material on your chest is compressible, which wool is generally not. There are, of course, other similar options besides the specific ones I mentioned.
The problem with compressing everything on your upper body like Archie suggests is that many kinds of insulation (down and synthetic down alternatives) retain body heat by providing loft to create dead air space. Compressing that air space eliminates the insulating ability of those materials. While a chest protector will cause that compression too, at least it does so on a limited area of your upper body, unlike a full vest. I suspect Archie was wearing a relatively non-compressible insulator, like wool, as opposed to compressible materials like down or PrimaLoft.
Allan