Time for Physics 101.
Liquid CO2 iscreated by increasing the pressure above 5.1 atmospheres, or 74.9496 psi. CO2 cannot exist in a liquid state at pressures above this point and must be stored in a suitable container or pressure vessel. As with all gasses, the temperature of the gas changes as the pressure on the gas changes. Increase the pressure and the temperature goes up, decrease the pressure and the temperature goes down.
Why does this matter? Simple, if CO2 is not kept at a suitable pressure it cannot remain in a liquid state and it would be far to cold to handle. Grab a co2 fire extinghuisher and feel the tank. Is it cold? No it is not, it is the same temperature as the surround air, or ambient. Do the same thing with your CO2 tank for your welder or your powertank that you carry in the back of your rig. It's not cold either. Why? simple the pressure in the tank is high enough to allow the co2 to exist in a liquid state.
What makes the CO2 cold is the pressure drop realized when the liquid leaves the tank via the pressure regulator. Put an air nozzle on end of a hose connected to you tanl and allow enough of a pressure drop for a long enough period of time and you'll see that frost will form on the side of the tank, the hose, and the nozzle itself. Now close the regulator down to the pressure you'd normally use for welding (12-18psi) and see how long it takes to achieve the same result. Hint: you'll be there for a quite a while.
So yes liquid CO2 is cold, but only when there is a suitable pressure drop as it leaves the container.