I have also had the worst cracking of hands and fingers in winter. Until this year!
In winter, I always seem to have some building project going on, vehicle or tractor repairs, plus the work in the machine shop, (Lathes mills and metal)
On week ends, I ski patrol which means working around the mountain and helping injured skiers, often with gloves removed to handle ropes, medical equipment, bandages and dressings etc. Cold and raw!
Though I have bag balm on my desk, (I live in Vermont for pete's sake, doesn't everyone have a can of Bag and Udder balm? ;-) I seldom use it. It's 99.7% petroleum jelly with a bit of coal tar antiseptic at a fairly high price. Bag Balm used to have camfor in it as well, but that was not approved for humans, the real market for BB.
I also keep a jar of Vaseline in the drawer. That I use regularly on both hands and FEET . Yup. my feet get dry in winter too. My wife gives me a tube of wussey hand and body lotion that I use daily. It has aloe. borage, and shea butter, (whatever those are) so if it fails to help my hands, I can use it for salad dressing.
Even with all these therapies and treatments, that I have been using for years, I would still had cracked,split and broken skin.
So let me get to the suggestion.
GET A HAND & NAIL BRUSH! Put one at every hand washing sink. and USE them. I like the natural bristle rectangular wooden handled ones, about 1" x 5".
Fill the sink bowl with very warm water, soap up. Scrub and scrub until there is only tender red skin. Dip into the hot soapy water often to soften the skin. Not even a dark shadow of dirt in the callouses should remain. Clean out those cut and splits too! It will hurt, but it won't hurt you! Hand washing should take as long as it takes to sing a couple stanzas of "Old MacDonald". (To yourself!)
Get that Skin Clean! If you get my point.
Chapped, cracked and broken skin is the product of bacteria that thrives on debris attached to your skin. Putting "healing lotions" on top is like "throwing bra'er rabbit into the briar patch".
I wash my hands just about whenever I complete the task that get's them dirty, even if that is just meal times or at the end of a full day outdoors.
Doctor tested! and it's working for me! One tiny crack on the outside of the right thumb just above the nail, not even open or red. ;-)
Try it! Hand and nail brushes are cheap!