Shoes
I started out using a pair of La Sportiva Crosslites: great, superlight trail shoes with big meaty lugs that fit narrow – maybe even a little too narrow, but then again I think I just bought the wrong size. Wonderful shoes. Too many trail shoes are overbuilt like hiking boots. Not these. This guy won a 100-mile trail race in them. They’re great for the road sections too. Mine went into semi-retirement around kilometre 600, when the black mesh started to wear out behind the rubber reinforcement at the toes [now living a second life as studded ice runners]. I’ve started using a pair of $30 Adidas trail runners from the Mountain Equipment Co-op clearance bin until I can replace the Crosslites.
Snowshoes 
I eschewed running-specific snowshoes for the Atlas 925 Trail. Though not really made for deep snow, they’re a good compromise between a running snowshoe (almost no flotation) and a backcountrys showshoe (bulky and heavy). Also, my size 13 shoes also don’t fit well in the bindings of the running snowshoes I’ve tried. I’m still looking for the right footwear to go with these.
Dog
A breed apart.
The purebred Alton Garbage Hound knows no equal as a backcountry companion. With a second stomach evolutionarily adapted to turn plastic shopping bags and discarded ice cream cups into pure kinetic energy, these dogs can run forever. Unfortunately, they are an endangered breed. I have only ever seen the one.
La Sportiva A.T. Grip Hobnail Grip Kit
The best solution I’ve found for winter running on hardpacked, icy trails. Described in detail in this post. Available here.
