I suffer from some arthritis myself and yes when the weather turns colder the arthritis tends to get worse and then gets better when the weather warms up again.
Arthritis and Joints do tend to hurt more in cold weather versus warm or hot weather but the cold weather itself is not the direct cause of the hurting joints.
When the weather changes from warm or hot to cold the barometric pressure changes and that change in barometric pressure change is actually what causes the joints to hurt.
During the cold winter months the barometric pressure starts dropping which puts pressure on your muscles and joints which then causes the pain.
So it has more to do with the drop in barometric pressure than it does with the temperature.