I don't think there is much difference. But "他们完全不会冷。" is more formal, meaning that they do not feel cold at all. You might want to stress "完全“ when you say the sentence to convey the meaning.
"他们都不会冷。" could mean exactly the same but the intonation would be a bit different - you are more likely to say it in a surprising tone as it's more of a spoken language.
A group of girls wearing skirts on a snowy day.
To express surprise, I would say to my friend: "他们都不会冷的吗?"
(my intonation would be in a surprised and teasing manner.)
Hope it helps!