The specific, and level of, solutes in the water determines the temperature at which it freezes. Fish are not perfectly permeable membranes, thus the internal freezing point of fish could be higher than the external freezing point of the water.
Fish are also cold-blooded and are at the mercy of their surroundings.
Human blood freezes at about -2degC. Brine can apparently go down to -20degC (source: Wikipedia).
If you make ice cream the old fashioned way you throw in rock salt to lower the temperature below 0C.
You can also chill beer cans sitting in water very fast adding piles of salt to water.
Available soluble salt ions lower the melting point of the water to the point where the water-ice would very much prefer to be salt-water at the same temperature. But a phase change requires energy, too. The energy required to melt the ice and dissolve the salt is taken first from cooling of the sugar-water in the cream, then from phase-changing it to solid crystals, then from cooling the solid-phase materials. If the setup has a paddle, that is mainly to transport heat from the center of the cream vessel to the conductive walls, and thereby regulate the size of the crystals.
Cooling beer cans in liquid water by adding salt does not rely on freezing point depression, but the heat of solution for NaCl in H2O, which also contributes slightly to the ice cream system above. You want cold beer fast? Use potassium nitrate (KNO3, saltpeter), as it has nine times the enthalpy of solution as NaCl.
What a hand-cranked ice-cream bucket might look like in ASCII diagram world:
|
o----o
____________|____________
\\.salt..|~~~~~|..salt.//
\\######| |######//
\\#ice#|cream|#ice#//
\\####|_____|####//
\\#############//
\=============/I also used to make it by putting the pot of cream mixture into a deep freeze still in the metal pot. Then get an electric hand mixer and mix it while it sat in the deep freezer. I'd do that over and over then for what seemed like 100 liters of milk and cream and hours of work I'd get 500ml of ice cream.