Would I put a rain coat on my dog? No. Would I put a winter coat on my dog? Depends. When living in Canada at -30º C I put one on. Here in Switzerland I don’t, not even in the alps at -10º C. This, because my dog has dense hair with wooly underfur for isolation.
As you can see there are a few things that you should consider and pay attention to before buying, because there is a huge variety in coats and not all dogs are the same.
A coat is certainly useful for a dog that has little to no underfur (e.g. Chihuahua, Dalmatian, Boxer, Weimaraner, Doberman), and walks predominantly on a leash. But if the dog in question is off leash, running around and playing, you should take off the coat. Since dogs, unlike us humans, cannot regulate their heat balance by sweating, it can lead to circulatory collapse faster, if you leave the coat on. Simply put it on after the fun time.
Also, if you put a warming coat on a dog that has underfur at mild temperatures (> 0º C), it can lead to circulatory collapse. However, some old dogs, or dogs with bone and joint problems will feel more comfortable wearing a warming coat.
If it is windy, a knitted coat doesn’t do the trick. Opt for windproof coats.
Last but not least: Behavior. A coat covers the largest part of the dog’s body and thus makes the body language „unreadable“ for other dogs. Strange dogs which don’t know dressed dogs, could react negatively to such.