Oh ok, in English we have both "midnight" and "middle of the night," the former is obviously an exact time and the latter just about any time at night. So, I got confused with miezul nopţii, which I translated in my head as "middle of the night".
In Romanian "miezul nopţii" isn't necessarly a very precise moment of time (It can mean midnight +/- a few minutes). But usually when one wants to express something less exact he/she can use "miez de noapte" (and that means sometime when it's dark (of course if there isn't a full moon when it's quite bright), nowhere near dusk or dawn).
Another way of saying it would be "in toiul noptii" which has the same meaning as "in the middle of the night". Not necessarily at 12 o'clock, but, as parakseno very well put it, nowhere near dusk or dawn.