There's nothing wrong with purchasing those coats that are typically made out of polyester, as many of them have great style and if you don't need the warmth a wool coat will provide, it may be the better decision for you.
If you're going out or to a more casual occasion, you may not want to wear your heavy coat as it could drag you down and may seem to be a hassle for you. A real leather jacket is a good choice as it keeps you warm but is not so heavy. This may also be the time for you to purchase that adorable polyester coat or even a wool coat that stops at the waist.
Winters can be long and harsh but we still like to be stylish with our outerwear so it's important to find a winter coat that is appropriate (in most cases warm) and fits out style. Although it can be challenging, it's worth the time, as you will wear these coats nearly all season and for a few years.