I guess he is using the Joule–Thomson effect.
- First, he compressed a huge amount of air in his lungs, increasing the pressure and temperature. He is somehow able to prevent the heat to spread in/outside of his body and prevent his lungs from rupturing.
- Then, he allow the air to expand rapidly by releasing his breath. The gas molecules do work as they expand, and this work reduces their kinetic energy.
- As the kinetic energy decreases, the temperature of the gas also decreases, producing a freezing wind.
Now, regarding the antibodies thing. I think he is able to manipulate his B cells to create any anti body he want. This is how he still has the antibodies from his past life, he learned how to create antibody at will, he was not born with them.
Either he is using a mysterious power (a skill instead of magic ?) to move the atoms in his body at will and create the molecules needed to quickstart the synthesis of new antibodies.. or he really has no mystical power, and he is somehow doing this trough sheer willpower.
In any case; even if he is a superhuman mutant, it seems like the energy required to do that kind of thing is huge, and probably could not come from chemical reaction only, so IMO he does have some kind of surnatural power at play, or maybe all that energy come from an alternate dimension or something.