Nah. Just dress normally and then put warm clothes on top (gloves, hat, a good coat, possibly some overtrousers for the rain) that you can remove at your destination.
Gloves needed at 0°C are reasonable. Sure, don't take gloves that let the wind go through.
I used to bike without gloves and a hat when freezing. Because I always lose them. The hands hurt, you end up being very cold. With appropriate clothes it's night and day, biking becomes enjoyable in winter.
> Just dress normally and then put warm clothes on top (gloves, hat, a good coat, possibly some overtrousers for the rain) that you can remove at your destination.
Great. I'm going to the mall. How do I remove my clothes while I'm there?
You put them in your backpack (or around your hips for the coat?).
Yes, you need a backpack or some sort of bag. Is it a big issue?
If it's not raining you don't even need the overtrousers and the coat might as well be the one you usually wear when it's cold. This coat probably has pockets big enough that you can put the gloves and the hat in them.
Gloves needed at 0°C are reasonable. Sure, don't take gloves that let the wind go through.
I used to bike without gloves and a hat when freezing. Because I always lose them. The hands hurt, you end up being very cold. With appropriate clothes it's night and day, biking becomes enjoyable in winter.