Depending on a professional environment you work in the attire does play a role in how fast/far you will advance. If you dress sharply you are more likely to be noticed by management and don't anybody kid yourself thinking that your hard work and skills will get you noticed/promoted. That's becoming more and more rare. It's all about how you present yourself. Yes you can wear a big puffy coat with a t-shirt underneath. Or you can wear a suit+tie and a wool coat.
See comment above regarding some corporate environments. In some cases it very much matters what others think because that is the only thing that will help you grow in a work place. Again, not the case everywhere but certainly some places.