This question is pretty straight forward... How to properly dispose of engine coolant? Should it be taken to a treatment facility like used engine oil or is it safe to pour down the drain?
Do not pour it down the drain, and do not pour it outside. Coolant is very sweet tasting to animals and they will "drink" it. It will affect both their kidneys and GI tract with potentially fatal consequences if not treated. Typical symptoms include vomiting, thirst, lack of appetite and unusual lethargy.
If you pour it down the drain, it will pollute things downstream from your sewage facility. If you have a septic system, it will foul it up.
Take it to a recycling/collection center.
Check your location's laws, but the EPA says it's not hazardous waste. If you're just a DIY-er, you can probably pour it down your toilet. Try and find a recycler first though.
In St. Louis, MO (my example), I have not found a better way for a DIY-er to dispose of it, but I believe professional shops have some way to dispose of it not accessible to us.
There are places in Missouri that accept antifreeze for recycling, such as Springfield and Clay County collection centers, but you have to be a resident with proof and there are limits on the amounts.
EPA, DNR, CDC etc.:
The EPA does not consider used coolant to be a hazardous waste. None of the major auto parts stores accept it for recycling. St. Louis, MO's household hazardous waste center does not accept it because it is not a hazardous waste.
The EPA (different link) says some states consider used antifreeze hazardous because after being run through your engine, it can contain lead, cadmium, chromium, mercury, kryptonite, etc.
Used antifreeze can be determined not to be hazardous by simply knowing where it came from. Testing is not needed to classify it as hazardous waste. If it has not been used in a old vehicle, heavy machinery, nuclear plant, etc., it can be called non-hazardous by whoever is disposing of it.
Here is a rundown of what is acceptable for each state including dumping it down the sanitary sewer. Some states have deemed it hazardous, but not most.
The Missouri Department of Natural Resources says, "if the facility is connected to a sanitary sewer that discharges to a Publicly Owned Treatment Works (POTW) and the wastes will mix with domestic sewage, the waste antifreeze may be disposed in the sanitary sewer on-site." And that exact text is seen repeatedly when searching about this subject. They do say you need to check with your sewer company, but since no permit is required, I assume that is legal covering their butts.
The CDC says that ethylene glycol will break down in a few weeks when not in our cars' closed systems, i.e. when exposed to air. Antifreeze contains more than just ethylene glycol though. It contains O2 inhibitors (buffering and alkalinity type stuff), but those will be depleted quickly when exposed to the open atmosphere. I do not know what chemicals it breaks down to though, but they are apparently not bad enough to mention. We're not chemists on this site so we should just follow the government agencies' policies.
Please open the two EPA links and search for the word "hazardous". The EPA does not consider antifreeze to be hazardous if it is not contaminated, i.e. it has only been used in a newer consumer vehicle.
Your local landfill may have a spot to dispose of oil and antifreeze.
In my city, it is illegal to dump antifreeze in the trash or on the ground.
Coolant is toxic. If human intake it then they will suffer soon and will develop cancer in a year. So it should be quite toxic to animals. In big picture, we should not produce such toxic liquid to begin with but just dumping in toilet is no good.