Yes the cold weather can make osteoarthritis worse.
But the cold weather itself is not the exact cause of the osteoarthritis becoming worse but a decrease in blood flow is one of the causes of osteoarthritis and other arthritis becoming worse.
Aside from the cold weather and the decreased blood flow another reason that osteoarthritis and other arthritis and joint pain becoming worse in the cold weather is because of the change in pressure in the air.
The change in pressure is the change in barometric pressure which increases the pressure on your joints which causes more pain on your joints and makes the arthritis as well as osteoarthritis worse.
Usually dressing in warm layers and covering the areas more where the osteoarthritis is can help increase the blood flow in that area and decrease the pain and make the osteoarthritis much better.