For standard testing procedures see either ASTM standards or USACE Engineer Manual 1110-2-1906, which can probably be downloaded for free:
Your tax dollars at work, or if you aren't in the US, OUR tax dollars at work. There may be some minor differences between ASTM and USACE - I haven't checked.
Correction? What are you trying to calculate? If you are trying to calculate pre-freezing porosity for example, you have to remember that unless you wash the salt out, the dry unit weight includes the salt, which contributes practically nothing to the volume of the pore fluid. Presumably you know the salt content of the pore fluid or at least the surface water.
I'm guessing that the marine sediments are fine-grained. For sandy materials, a 20% difference in water content would be a major difference, but for clays from different sites, it might not mean a whole lot. Do you have Atterbergs? For comparing water contents of materials from different sites, it is sometimes useful to employ the Liquidity Index:
LI = (%w - PL)/(LL - PL)
(Equals 0 at %w=PL; 1.0 at %w=LL; 0.5 halfway between.) Clayey materials with different clay properties but similar deposition and stress histories could have very different water contents but similar LI. Materials with similar LI would have fairly similar engineering properties, and for soils from different sites, you would expect greater similarity for a given value of LI than for a given value of %w.
I don't see how the freezing point would affect what happens to the water content. There is the issue of evaporation (sublimation, directly from solid to vapor) of water out of the samples if they are kept too long, kind of like frozen vegetables that get dried out even though they are surrounded by frost in the bag.
Regards,
DRG