You don't mention what kind of walking that 1 mile will be. If it is not technical, a Pac boot is definitely the way to go, they are way more comfortable than a mountain boot. If it gets too vertical, then a Pac boot will make that mile a tough one. Either way, a double boot (removeable liner) will be the warmest whether you are looking to be out 1 day or multiple days. In a Pac boot, some good options have already been mentioned. In a mountaineering boot, you would want something like the La Sportiva Baruntse with a removeable foam liner boot. You can also find used plastic boots like the Koflach Arctis Expe pretty cheap.
As mentioned earlier, If your feet are getting cold, check the insulation on the rest of your body as well. Make sure your cold weather boots don't fit too tight, either.