I'm not sure about pocket dimensions, but if you want to form water really quickly from H₂ and O₂, just light a match. Certainly, rockets are propelled by mixing liquid oxygen and liquid hydrogen, but they are ignited beforehand. I am unsure what would happen if you mixed liquid oxygen and liquid hydrogen (and low temperatures) without first providing enough energy to start a chain reaction (that is, lighting them on fire).

So far as we know, real life force fields and pocket dimensions do not exist.

H₂ and O₂ form water very quickly and easily when combined in gaseous form - so much energy is released in fact that the combination is explosive. The explosion and fire that destroyed the Hindenberg was fueled by hydrogen in the blimp catching fire and burning, using the oxygen in the air.

You would not be able to keep temperature low while burning hydrogen with oxygen. The reaction puts out so much energy that it is, simply put, a fire. Fires are hot; it's their nature.