Two things damage Tung oil. Air and moisture.
And usually, you get it in polyethylene containers which you squeeze to remove all but the last bit of air in the neck when you put the lid on and then pour into a smaller marked polyethylene bottle when the empty space is too large to remove the air. Another technique is to drop marbles in as the fluid level decreases, extract for reuse on the next bottle.
The moisture causes it to get cloudy, the air causes it to start setting up.
The bottle I had in outside storage over winter is its natural clear honey-colored self and is doing quite well on the tool handle I just applied it to. Being an oil, it would have to get pretty cold for it to gel, but that will only last as long as it's that cold.