Do you mean the skin around your nails? If so that's the eponychium which is misidentified as the cuticle. Then again who can say or remember eponychium lol? Seriously though, the skin around the nails is very tender and thin, similar to your eyelids being tender and thin, and as a result needs to be pampered. Best thing to do is to give yourself an oil hand bath once at least once a week in the winter and wear gloves when possible even if it's not super cold outside. A pair of cotton gloves to wool gloves to leather gloves - any to keep the cold, dry winter air off your hands is best. At night if your skin is really bad then try some kind of thick lotion or cream and wear a pair of non-latex gloves for an hour before bed and allow your skin to absorb it.
It's the industry who misleads people into thinking it's called the cuticle. No oil or product will soften or get rid of the real cuticle but let's face it, how many can properly pronounce eponychium much less spell it. LOL
Semantics aside, I think LUSH Lemony Flutter is one of the most moisturizing butters out there. Maybe that would work for you. Also, there are ways to care for your skin from the inside out. Vitamins A, C, and E, Zinc, and omega 3's are all great for skin health. Staying hydrated is important as well.