The cause is the relatively good driving conditions; the effect is that they didn't arrive too late.
Actually, the driving conditions were bad. That is the problem I have with "as". One would expect someone to arrive late with bad driving conditions. That they didn't arrive "too late" sounds as if it were unexpected. I think I would choose "given that" to begin that sentence.
The problem with this question is the vagueness of the language. What exactly is "rather bad" or "not too late"?