Interesting question. Wool is a poor conductor, which is precisely why people weave wool into clothing. A knitted wool sweater is warm because it creates a layer of "dead air" around its wearer. Since people are warm-blooded, as are all mammals, the warmth from our bodies heats up that layer of air in the sweater, helping to slow down the flow of heat from ourselves to the environment. In other words the sweater helps keep us warm.

If the sweater were made of a good conductor--the metal of a suit of armor, for example--heat would readily be transmitted to the environment.

As to why wool is a poor conductor, and most metals are not, I'll leave that answer to the physicists, but it's related to how easily electrons flow through these substances.

You should do an experiment and find out! If something conducts heat, then it will allow heat to move from a warmer place to a cooler place. If it is not good at conducting heat, then it will prevent heat from moving from the warmer place to a cooler place.

So what you should do is take a pot of hot water, and wrap it up in a nice wool sweater. Then measure how long it takes for the water to cool off.

Then, repeat the experiment without the wool sweater, and measure how long it takes for the water to cool off.

If wool is a good conductor, then the water in the pot will cool off as fast or faster with the wool than without.

Wool is a good insulator. That's why we wear wool sweaters and jackets to keep ourselves warm in cold weather. If wool were a good conductor, it would transfer the heat out of us and to the cold outside.

Here's what the internet says:
Sheep wool insulation is an outstanding insulator. ... Due to the crimped nature of wool fibers, they form millions of tiny air pockets that trap air, helping to provide a thermal barrier. Thermal conductivity is the ability for heat to pass from one side of a material through to the other.

read more here

Wool is not a good conductor of heat. To be a good conductor of heat, a material needs to allow heat to pass through itself quickly, and this trait requires that the atoms (very small fundamental particles) of a given material be able to collide with each other freely, and that the electrons (even smaller particles in all materials that are negatively charged, electrically speaking) can move freely.

Metals have atoms and electrons that can collide and move much more freely than materials such as wool, so wool does not conduct heat well, while metals do - this is why wool makes good insulators for humans in the winter, to help us keep the heat in our bodies from dissipating.