Plasma is so low density, so the total heat capacity will be quite low. You’d need a lot of cold plasma to chill a very small amount of liquid water through freezing.
Remember that a plasma is an ionic gas, so it doesn’t have a specific temperature associated with it. It’s just a bunch of free charges (ions, electrons, protons). Assuming the bulk charge of the plasma is effectively neutral, then you have some limits on density. If they get too close to each other, they start binding to one another. At cold temperatures, it is much easier to collide and stick than at hot temperatures, so cold plasmas tend to be even lower density than hot plasmas.
Which means, it cannot absorb much energy, because there isn’t a lot of matter in it. Sure, you could cool something with it, but it would take a lot.