Piping in because I'm someone who prefers to bike in normal clothes as much as possible and so my preferences are very different from others stated here.
Now I have a bike with an internal hub/chainguard, so I don't have to worry about my pants getting caught in the chain. I can bike to work in whatever I'll be wearing that day. But before I had this bike, I used to tuck my pants into my socks or use one of those pants straps that you can often get for free. I haven't been caught in cycling tights in YEARS.
I LOVE wool for biking. I much prefer it over synthetic fabrics. Wool doesn't get smelly, wicks sweat and is otherwise amazing. I wear wool underwear, wool jacket (just a normal one), sometimes wool pants. Normal pants, not cycling tights.
But as others have said, with a longish commute (more than a mile or two), keeping cool is key because your body generates a lot of heat while biking even in cold weather. When I first leave the house on a winter ride, I'm quite cold. But I soon warm up. Winter is one of my favorite times to bike! For 40 degrees and warmer, I just wear a cotton bandana over my hair and under my helmet. I can easily adjust it to cover my ears or not as needed that moment. Colder than that I wear a thin wool cycling cap with ear flaps under my helmet. Depending on how your bike shifts, you may be able to get away with mittens instead of gloves too.
I'm a BIG believer of not needing cycling-specific clothes. I think 99% of people can figure out biking in all seasons with stuff they already have in their closet.