I take the wisdom of the best survivalist/bushcraft expert Les Stroud aka Survivorman....his famous line is "if you sweat (dramatic pause) you die".

Ya'all get some brutal cold up there so I might have slightly underestimated the need for warmth when you're less active but I kinda fixated on your biking commute. A three mile commute should be 20-30 minutes depending on things like sitting at traffic lights...pretty sure you'll be warm by mile 2. Casually walking will require significantly more warm layers, or ideally a parka like the ones others are recommending.