I'm still getting out some (call it cold weather work release), but it's definitely a challenge. First thing to think about is how to dress for these conditions without freezing all sorts of skin and body parts.
Pictured is my wardrobe for a snowshoe run at -30 F.
From toes to head, the list includes:
chemical foot warmers
neoprene foot covers (for snowshoe running at least)
lycra half tights
wool lined and extra thick "arctic tights"
xc ski pants with windbreaker front panel
3 polypropelene shirts
windbreaker vest over the first polypro shirt, beneath the other two
xc ski parka, double layered and breathable
xc ski gloves (lobster claw)
chemical hand warmers
neoprene face mask
2 wool-polypro hats
On New Year's Eve I snowshoe ran for about 5 miles, which took about 55 or 60 min including a couple stops to take some pictures of the trail and scenery. I never got cold, but wasn't over-dressed either. I was feeling the chill after 30 or 40 minutes. At this temperature it's more of a slog/slow jog and I don't even think about speedwork or tempos. At -10 or -15 I might do eight or ten pick ups of 20 to 30 seconds, just to keep the legs from getting too stale. But at -30 it's all about survival and keeping your feet moving so that you can get back for some hot chocolate. Or wine.
Now a lot of people would think that we're crazy to live under such conditions, let alone go outside to train. But rather than thinking that you're a prisoner to the elements, you learn to adapt to if not embrace the silence and the beauty.