"Soak each other" would mean that they pour water on each other and get their clothes thoroughly wet, in my interpretation. In that case it should be "soak each other with water". You could soak a piece of clothing in water by immersing it and leaving it there for quite a while, but you wouldn't do that with a person.
"Soak mutually in water" to me would mean that sit in a tub or pool (or pond) together and soak in the water. "Mutually" is an odd choice of words there but it's possible.
"Soak through in water" doesn't really make sense to me in this context.