I have been using Stegar muckluks for several years now and will never go back. They are very light weight, EXTREMELY COMFORTABLE and always warm. The only disadvantage is when you break through ice. They are not 100% waterproof. But even when your feet are wet in muckluks they stay warm:)
I have used Steiger MukLuks for several years. Make sure you spray them with a water repellent. They are not waterproof or even very water resistant but at the temps. up north they do exactly what they are made to do. Keep your feet warm and allow them to breathe. I carry a set of tingleys in the spring for slushy days that I can slip over the mukluks. Problem solved. I have not found anything as warm as mukluks for snowshoeing.
"With an ax, you can build a life. With a stove, you can boil water. That is if nothing breaks and you don't run out of fuel." -Samuel Hearne
Steiger mukluks are the way to go... in temps lower than 28deg F. I have a pair that is 8 years old and still in working condition. During the winter months they are used almost daily. I have only broken one strap (easily sewn back on) and just recently started to have some break-down of the sole. The soles will get "gummy" if you use them everywhere as I do.
Steger Mukluks also: I am on my second pair and they are still the best. I have a pair of the Empire Canvas Works and they are a distant second but useful. Tingle Boots also with felt liners and 1 or 2 insoles for wet & slush. Neos are also fine like the Tingley. For snow shoeing I use classic wood snowshoes with a homemade lamp wick binding. This is the best system I have used so far. Going to the mountains? That's a different ball game and need for commercial shoes with metal cleats.
I think those boots would be great for using over mukluks in slushy conditions that exist on early ice. I guess not being water proof is the down side to mukluks, and those NEOS would solve that problem.