Yes cold weather can cause back pain and other pain in your body because muscles, tendons and ligaments that support the spine to tighten during the cold weather.
When a drop in barometric pressure happens that can also cause joints to swell which can cause pain.
I have back pain and I know when it gets cold like now and I'm out in the cold weather that my back starts hurting worse and that's because of the muscles tightening when the cold temperatures are in the air.