When I set a snare, I use a "pin", whether made from a piece of wood or a nail. The noose is either connected to the pin (which keeps the limb from being pulled up), or else I use a separate "bait cord" which runs from the bait in the center of the snare to the pin.
In either case, when a critter sticks its head into the noose and starts pulling on the bait, the pin is pulled, freeing the limb to fly up, which pulls the snare tight around the poor critter's neck. The limb then jerks it up, where it hangs until it either dies or breaks free.
What Samurai Jack is doing, I don't know. I suppose one could tie smaller "trigger pin" cords all along the inside of the snare's loop, so that when they were stepped on, they'd pull the pin loose... I've never seen it done that way, though.
As for man-trapping, in general, it is certainly possible. The VC in Nam were very good at it, and incorporated sharpened limbs to either smash into you, like a morningstar, or the snare noose would sling you into a tree whose limbs were sharpened, kinda like a wall of spikes. Even nastier surprises were available with more modern technology. One very old trick was to coat all the spikes with a mixture of blood and horse feces... This pretty much insured a major blood infection for anyone who got poked, and in the jungles, that was usually a death sentence...
