Your
boat engine's
cooling system works very much like your car's
cooling system. There's the water that circulates within the engine block that removes heat from the cylinders. But then, there's another, separate water system that removes heat from the engine block water. In your car - the heat is removed from the engine block water by the radiator - which uses a fan to draw (relatively) cool air over a series of tubes through which the hot engine block water passes. Excess heat is removed by
heating the cool air.
In your boat engine you have the (fresh) engine block cooling water that you fill via either the radiator cap on the reservoir or an expansion tank (which I don't see in the pictures of your engine). You'll have a pump on the engine that circulates that water throughout the engine. It may be below the fresh water reservoir and out-of-sight in the pictures of your engine. It will be run by a 'v' belt on your engine's crankshaft pulley. You put antifreeze in that system just like you would in your car.
You'll also have a 'raw' (salt) water cooling water system. That system is a flow-through system that gets its water from below the boat. It comes in through a thru-hull fitting, passes through a filter and enters a heat exchanger. The
raw water pump is also driven by a 'v'-belt off the crankshaft pulley. Yours is the one to which a green
elbow and hose are attached.
That cool
raw water circulates around a series of tubes inside the heat exchanger through which the hot engine block water passes - being pumped by the engine
water pump. The now-hot
raw water exits the heat exchanger and is (usually) introduced into the exhaust system through an exhaust
elbow before the
muffler. The excess engine heat is removed by
heating the raw water in the heat exchanger jacket.
You add antifreeze to this cooling water system just as you describe. Shut off the thru-hull valve, open the top of the filter, start the engine, and add antifreeze to the filter until you see the antifreeze coming out of the exhaust pipe. Otherwise, you can take a hose off the filter and have the engine pump antifreeze from the jug it comes in or from a bucket.
The engine cooling system shouldn't have frozen if you've only had a day or so of below-freezing temperatures if the boat is still in the water.