Ice magic lowers the temperature of things. I was thinking of freezing the water in blood (specifically blood plasma) to kill. How would this work? Also, can it be used on non-mammals, like sea creatures or amphibians?
Sure. Blood is just water, with some impurities added. Same whether it is human, or fish, or even insect. All animal life's blood can be considered 80-90% pure water. All plant life's 'blood' can be considered 95% pure water, suspended in a spongy substrate.
Just remember that the phase change from liquid water to ice requires a LOT more energy than just cooling the blood. Cooling water from 0C(liquid) to 0C(ice) takes the same energy as cooling water from 80C to 0C(liquid) in the first place.
So for the same effort (energy requirement), you can either instantaneously fully cook a fleshy being(to the point of overdone), or halfway freeze its blood.
Freezing the blood is very excessive. Even if it's localised, like in the throat, you require a lot of energy. While killing by preventing blood flow in the larger and smaller blood vessels, or damaging the vessel walls due to pressure or fractured ice, it's literally overkill. Hypothermia will do the trick. @MarvinKitfox refers to this well.
With only a few degrees change of the blood, the whole body will cool down. These effects will reduce the effect of many enzymes. This will basically incapacitate your opponent, killing her/him if left untreated.
This would work on any warm blooded creature. Cold blooded creatures can be affected as well, but are more resilient to drops of temperature. If you go for truly freezing, you can kill most worthwhile creatures. With worthwhile I mean man, snake, bear and spider. Not Tardigrades.
How it would work? It's magic. As @L.Dutch-ReinstateMonica♦ mentions, you can make it do whatever you want. Cooling in the real world is transferring heat away from the place you want to cool. You can also have the magic simply stop the molecules moving/trembling, removing the heat altogether. Find a nice way how to do that and you're golden.
Yes and no. Because the Plasma is mixed with everything else in the blood it per se can't be frozen by itself, but if you can could it down enough you should be able to freeze the blood itself, as it essentially would act like salt in water and lower the freezing temp (which is -0.5 C°) which is negligibly blow the freezing point of water.
I wouldn't see why this shouldn't work for sea creatures of amphibians. The only problem with sea creatures may be that the water around them might "leach of a lot of the cold", i.e. distribute the warmth enough to stop them form freezing.