A good cable doesn't need ferrite around it. But it might make a cheap cable better. As for winding it through and around the ferrite: that would depend on what you want to do with it. It mostly makes a smaller ferrite core function better, so it's only about cost reduction.
Some background: if you take a plain, dual-wire cable that carries the signal and ground, it suffers from EM interference. You can shield it, which takes care of the interference, but makes the cable more expensive. Another way to remove the interference is, to have one wire carry the signal, and the other one the opposite (negative) image of the signal. Like, when the signal is +1 V, the other one will be -1 V. And when the signal is +2 V, the other one will be -2 V. That way, any interference will have the same impact on both, and to restore the original signal, it is sufficient to use the difference between them as ground. Other solutions alike that one are used as well.
The first type of cable (shielded) is best, but it does create impedance (resistance, -dB). And it is more expensive. That's why we use UTP (Unshielded Twisted Pair) as Ethernet cables. And the "Twisted pair" bit is because you want the signal pairs to be as close together as you can get them, and as equally exposed to the interference as you can make them.
As for the ferrite cores around the cables: they damp high peaks in the signal. They cause a moderate bit of impedance (which reduces the quality of the signal a bit), but remove sharp peaks that might damage the electronics.
As all monitors and televisions nowadays are auto-adjusting, the peaks are filtered in any case. So you're left with the choice between shielding and unshielded. Which is only a problem for signals over medium or long distances and severe EM interference. So you choose shielded for those, and unshielded, but good quality twisted pairs for everything else nowadays. Add some more grounded wires to be able to make pairs, if required. Even without using opposite signals on both wires that make up a pair, you get a good signal by using a comparator between the ground and signal ones to extract the signal.
You could compare the ferrite coils with a blur filter: it smooths everything out a bit, including the signal itself. So they don't improve the signal quality.
