This is either a long-tailed weasel (Mustela frenata) or a stoat/ermine/short-tailed weasel (Mustela erminea). The ermine has a more northerly distribution than the the long-tailed weasel, but both species do have have some overlap in their ranges.
They are easier to tell apart in the summer coat. Long-tailed weasels have a more yellow belly than the ermine does (and their tails are long and whip-like).
I have a specimen of what I believe to be a long-tailed weasel in my freezer. It was killed in Central West Virginia in late October. Its legs and belly are white, but its dorsal area and head are still dark brown.
It could be a stoat that wandered a bit to the south, but because of its more southerly location, my money is on it being a long-tailed weasel.
I think the animal in the video is a long-tailed weasel, not an ermine/stoat.
Not all populations of ermine/stoat turn white in winter, although I think all North American populations do. Long-tailed weasels that live in the southern parts of their range don’t turn white.
The long-tails live only in the Americas, and they make it as far south as Bolivia. Somehow, I don’t think the Bolivian weasels turn white.
One thing it is not is a ferret.
Update: Here’s a Mustela erminea in its winter coat. I think we have a long-tailed weasel in the video.