How much carbon is sequestered out of the atmosphere through marine snow?
This probably doesn't answer your question but might help the thought process:  

The part of the carbon cycle you are inquiring about is referred to as the biological carbon pump.
Phytoplankton total net primary productivity is estimated to be ca. 45 to 50x1015g of (fixed) Carbon per year (Falkowski et al. 1998). In comparison land plants are producing an estimated 50 to 60x1015g of (fixed) Carbon per year (Field et al. 1998), hence a roughly 50-50% situation.

Of course not all of it is being buried: some is being recycled by heterotrophs and some decomposed (and thus released). 

As far as the zooplankton and zoonekton (fishes, marine mammals, swimming molluscs and arthropods,...) are concerned, although I do not have numbers to back this claim, I would assume their impact on the carbon cycle to be (necessarily) smaller than that of the phytoplankton (since the carbon they are exporting comes, ultimately, from recycling the phytoplankton).

Source:
Falkowski, P. G., Barber, R. T., Smetacek, V., 1998. Biogeochemical Controls and Feedbacks on Ocean Primary Production. Science, 281: 200-207.
Field, C. B., Behrenfield, M. J., Randerson, J. T., Falkowski, P., 1998. Primary Production of the Biosphere: Integrating Terrestrial and Oceanic Components. Science, 281: 237-240.