Is it true that protons bind with electrons at low temperature?

Free protons will bind to electrons at sufficiently low temperatures. However, the character of such bound protons does not change, remaining the same. A fast proton moving through matter will slow down while interacting with electrons and nuclei, until it is captured by the electron cloud of an atom.

The result is a protonated atom, which is a chemical compound of hydrogen. When free electrons are present in a vacuum, a sufficiently slow proton may pick up a single free electron, becoming a neutral hydrogen atom, which is a chemically free radical. Such hydrogen atoms tend to react chemically with many other types of atoms at sufficiently low energies.

As free hydrogen atoms react with each other, they form neutral hydrogen molecules (H2), which are the most common molecular component of molecular clouds in interstellar space. Such hydrogen molecules on Earth may then serve as a suitable source of protons for accelerators (similarly used in proton therapy) and other hadron particle physics experiments that require protons to accelerate. One of those experiments and the most powerful happens to be the Large Hadron Collider.