I've had the same problem for years, it's actually been diagnosed as exzema... but it gets a lot worse when the cold weather arrives.
The only moisturizer that has worked for me, without feeling to greesy or causing irritation, is Cetaphil lotion.
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And as far as gloves go, nitril powder-free has worked better for me. Be careful though, your hand will sweat with the gloves on, after removing them you should wash your hands (or at least rinse with water) and moisturize right away or they'll really dry out.
I worked as a mechanic for years in Oshkosh, Wisconsin. The solvents, oils, chemical and cold just ruined the skin on my hands. Now any kind of trauma , clapping, twisting on a screwdriver, hot water, cold weather etc. will cause an outbreak and that leads to severe cracking... very painful.