A:Sort of depends on the climate. Are we talking cold and dry or cold and damp?
If cold and dry, then something down-filled is the clear winner. Probably the leading sub-$300 candidate here is the Mountain Hardwear Sub Zero SL Hooded Jacket ($280). A classic design, executed well. Full hood, 650-fill down. And it actually has a waterproof/breathable laminate shell so is pretty good when it's damp. Another very strong candidate is the Mont-Bell Permafrost Light Down Jacket for women ($250). Lighter than the Mountain Hardwear piece, with 850-fill down, and an excellent Gore Windstopper shell for great breathability and decent moisture-repellency. Weighs only 14 ounces.
If conditions are damp, then I lean a bit toward a synthetic-fill parka-type piece. A good one is the Patagonia Women's Nano Puff Hoody ($199). It's a trimly cut piece that has very soft, warm PrimaLoft One insulation, which keeps you warm if it's wet or damp. Also has a naturally water-resistant polyester shell.
A third option is a so-called three-in-one, a jacket combo with a zip-out inner piece. Those can be pretty warm, and quite versatile. A good example is the Columbia Whirlibird Parka 3:1 ($200). It has a waterproof-breathable shell along with a zip-in liner that has polyester-fiber insulation. It's a nice piece, and better looking than most insulated parkas.