Dante doesn't have a choice whether he wears coats or not as he has to wear his Service Dog vest at all times when he is out with me.
With small breeds of dog - like Monet and Dante - it is essential that they wear a coat in cold weather. In conditions such as snow, it is also advisable for them to wear tiny boots. If they don't, they can get a condition called Hardpad which is very painful and difficult to cure.
However, I would not "dress up" any dog in some of the ridiculous clothes that I have seen for sale in pet shops.