What's the temp? What's the breed?
It all depends. It gets cold as all heck here-but many dogs don't need coats. And many do.
And tbh even if 15c is as cold as it gets if the dog is cold-he needs a coat.
So is your dog shivering? Shivering is a last ditch effort to save body temperature. Basically when a wild animals shivers-they are done. Obviously not the case with our furry friends as they can come inside but you need to realize shivering is serious.
SO if the dog is shivering-definitely needs a coat. And possibly booties-look for your dog holdilng up his paws.
None of this has to be expensive. Dog clothes are cheap now=and even cheaper is finding a sweater in your closer and making a few stitches to make it a bit smaller (and if you have a boy dog-trimming it so it does not get peed one) and voila