It would go out. In a room cold enough for Oxygen to turn solid, there would be no gaseous oxygen to sustain the match’s combustion as it falls. The wood would have some latent heat, but not enough to re-ignite itself in a room that cold.
Pure oxygen won't burn anyways. What would it oxidize? If you had frozen a mix of oxygen and hydrogen (without the two separating) it would be possible to ignite and burn it.
