Interesting timing. I am sitting here with my Steger Mukluks on. Mine are the Tall Ojibwa. I have been playing with them and will be wearing them to snow shoe with toward the end of next week. I have been trying them with different socks. I have had them about 12 years but haven't worn them in several years.



They work well for snow shoeing once you get your snow shoes set-up for them. As for running I never tried that but the soles on mine don't have much traction. I have walked on ice as on a frozen lake with little trouble but don't think I would try running on ice with them. The Steger Mukluk are very are durable. If you could attach a traction device of some type you might be able to run in them. Yak-Traks might work but I think you would have a problem keeping crampons tight.
The mukluks come with a wool felt bootie and a wool felt insole. If you add a good wool sock that may be enough. Running should help keep your feet warm.
I am going to try my RBH VB socks and see how they work. I will find out first if my feet sweat enough to make the VB socks necessary. Steger says the Mukluks will breath. How much I don't know. I should be wearing mine everyday for a couple of weeks.
The Arctic Mukluk uses the same sole material but has deeper cuts in it for better traction. Foot support while running needs to be considered also.