Muscovies are really hardy ducks, but as kuntrygirl asked it really depends on how cold you mean. They are originally from South America so they evolved to live in hot, humid climates but do so well in others that they are now considered a feral/invasive pest. They do well where I am which is the Los Angeles desert. We have hot, dry summers that hit about 100 degrees or more and the past two winters have been very rainy and very cold (for us, anyway lol) that got down to about 30 degrees or lower at night.
Mine have survived -25 with blowing sleet/snow. As long as they have a place to get out of the wind & stay dry, they will do fine. In the winters, I use 4 x 4' apple bins, flipped upside down and filled with straw. As for their waterers, I use buckets that are too small for them to swim in. The only time I've had issues is when their feet get wet and it's below zero out. Then they tend to fall off (their feet). But since changing the way I water them and locking them into their shelters when it's really nasty out--no problems.
Please expand on this....Meaning they need boots??
Seriously though, is it a problem with scovies? Where I live...their feet are gonna get wet
It's a problem with all waterfowl. They don't have much feeling in their feet so they don't seem to notice when they are freezing off.
If you have no practical way to keep them out of water or wetness during very cold weather, you could consider putting them on wire for the winter & wrapping the hutch or whatever in plastic on the sides to keep them out of the wind. Mine are out in the snow all winter, unless it's below zero or super-windy...then I lock them up.
Here are mine in March:
Here is a shot of their pens & shelters in the summer:
During the very worst weather, my stupid geese would not go in their shelters at all--so I had to grab them and ended up putting them in my horse trailer for a few days. The ducks, I shoved into the shelters and used a straw bale to block their doors--so they were locked in there overnight.