I am almost 80 and I too have stiff painful fingers which contribute to a weaker grip. I also have "triger finger" which can be very painful. My chiropractor says I probably have tendonitis and/or arthritis and advised specific exercises and gently gripping a warm item. It helps a bit. I also wear padded cycling gloves when using tools ( ... and when cycling on my recumbent trike) which helps reduce pain from extended gripping.
Regarding the effect of cold I seem to remember from my student days that in cold weather the blood flow to the extremities decreases to conserve body heat. This might be a factor?