I don't think your statement above is accurate. The overall effect of La Nina could be a slight reduction of global temperature this year. This entire year. Over the entire globe. That doesn't mean that seasonal changes won't happen.
that stated "la nina" somehow churns up the cold from the deep ocean and cools the atmosphere with it. Insane stuff that my tax dollars pay for. Do you agree with the theory or do you have another explanation for how your la nina fallacy cools the earth? If so, be specific about what it does with the heat. Where does it hide or sequester it?
The best I can do is show you diagrams of how La Nina works. Note what happens to the thermocline in the Pacific.
Normal situation: 
El Nino condition: 
La Nina condition: 
Based on these diagrams, do you see where the cold surface waters of a La Nina event come from? Is there anything else I can add that would substantially improve your understanding?
Bonus question: what happens to the thermocline in the western Pacific? What might this mean for the heat storage capability of the Pacific water column?