You may have several things going on here.
Your white hands when walking may be similar to those symptoms experienced by runners. Blood is not pushed out to the extremities so effectively when exercising, especially during fairly vigorous exercise. If it only happens when on a long walk then I suspect nothing much is wrong.
It may worsen, though, as the cold weather sets in and if that is the case, perhaps consider taking some Ginkgo Biloba as this is known to improve peripheral circulation in conditions such as Raynauds ("white finger") and chilblains.
Your other symptoms may be signs of Rheumatoid Arthritis, although we are unable to diagnose and so I'd encourage you to ask your GP.
Rheumatoid arthritis can affect people of any age and usually affects both sides of the body, so both hands, both wrists, both thumbs, etc, as you describe.
It can resolve itself after a number of years but involves unpredictable episodes of pain in the smaller joints as you too describe. Please consider eating oily fish 3 times per week (a tuna sandwich counts too), as Omega 3 oils are known to control inflammation and try Atrosan Devils Claw tablets, which are licensed for Rheumatic and muscular pain.
I hope this helps