If you use over the ear headphones while walking, skiing or bicycling, it will be difficult to keep them warm. A few years ago I got Bose QuietControl 30 semi-wireless buds, and they are a lot easier to keep warm due to their size and shape.

The battery, and most of the electronics are around your neck, so you can easily protect them with a scarf. The buds are smaller than headphones, so they can be protected with a proper hat.