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By now, most people have heard about the two individuals who were rescued on Mount Lafayette. If you haven't, read about it HERE. In brief, two trail runners ended up losing the Greenleaf Trail as they descended Mount Lafayette. One of them allegedly lost their trail running shoes in the process and ended up barefoot. As an objective party, I have no idea what kind of shoes they wore or what they brought with them, but judging from the fact that snowshoes were not mentioned in the article, I am going to assume they did not use them. But based on many, many hours of personal experience in these mountains, I can tell you that ultralight trail running the 4000 footers is a very, very bad idea.
First, let me preface with this: trail running in winter can be done safely in the mountains. I won't lie either. I don't carry a sleeping bag and pad with me on winter hikes/runs. But I do..
Buy my new novel Take to the Unscathed Road now!Follow me on Facebook, Instagram, and Twitter!
By now, most people have heard about the two individuals who were rescued on Mount Lafayette. If you haven't, read about it HERE. In brief, two trail runners ended up losing the Greenleaf Trail as they descended Mount Lafayette. One of them allegedly lost their trail running shoes in the process and ended up barefoot. As an objective party, I have no idea what kind of shoes they wore or what they brought with them, but judging from the fact that snowshoes were not mentioned in the article, I am going to assume they did not use them. But based on many, many hours of personal experience in these mountains, I can tell you that ultralight trail running the 4000 footers is a very, very bad idea.

First, let me preface with this: trail running in winter can be done safely in the mountains. I won't lie either. I don't carry a sleeping bag and pad with me on winter hikes/runs. But I do have an emergency bivy with me at all times, lighting, and traction based on what I know the conditions will be like. Evidently the "trail runners" on the Franconia Ridge Loop didn't think to bring snowshoes just in case there were drifts, and this could have been fatal had they not been rescued in the nick of time.
Can you do these peaks in winter with trail runners? Sure. But they have to be waterproof at a minimum, and insulated unless you're crazy. Especially on a day with near zero temps with wind chills below zero. They do make these kinds of shoes, but they are not cheap because they cater to a very specific type of athlete, and not many people are trail running big mountains in the dead of winter.
Which leads me to my point. Ultralight trail running the 4000 footers is a silly idea. To me, unless you have the bare minimum of three layers (combo of down, fleece, waterproof layer), an extra pair of socks, multiple pairs of gloves, multiple hats or balaclavas, insulated and waterproof footwear, appropriate traction, and a water resistant pant layer, and enough food and water to last a night, you're putting yourself and rescuers at risk. 
Winter rescues don't always have happy endings, and even when they do, the rescued often have lifelong consequences such as frostbite and nerve damage at best, amputation at worst. So if you're going to trail run in winter in the White Mountains, don't be brazen.