Well, I declare myself totally unqualified to answer this one. I'm heading for summer right now for a start, and winter in July did not include snow.
But my first stop for coats-that-suit-the-location is any second hand shop, and my first stop for shoes-that-last-forever is either Redbacks or Doc Martins.
But like I said, not qualified.
Hey that's actually the best answer. The best people to tell you what will fit the weather is the actual people living in said weather. While there is some overlap in some cases there is literally no-one more qualified than them to answer this question. Like I have plenty of experience with the Canadian winters but I really have no idea what a German can expect in Berlin.
I see your budget is in euros. What country are you in? That might help with recommendations.
I'm from germany (as per my instance xd) So European market
I’ve tried a LOT of different brand winter coats, and my favorite hands down is Fjallraven. I have the Skogsö Padded Jacket, and wear it more than any other. Now you’ll need something warmer for the temps you are talking about, but they have what you need. They also will do repairs if necessary.
For practical, durable and quality made products that are made to last.