The Antartica is the vast source of cold on our planet,just as the sun is the source of our heat, and it exerts tremendous control on our climate. How would I paraphrase that

Look at the key words:

Antarctica, cold
sun, heat
they have a lot of control of our climate

To paraphrase the given statement, you could say:

"The Antarctic region acts as a significant provider of cold temperature on Earth, comparable to how the sun serves as the primary source of heat. It plays a crucial role in influencing our climate."

I can't tell you how YOU would paraphrase that statement.