I can't imagine this is a diaper related problem, but I can see a new parent having some relevant circumstances change:
- You're around children you want to protect from germs
- You're around children that are constantly making messes
- You may have your hands in water more from giving baths or hand washing baby bottles, dishes or clothes
1 & 2 mean you wash your hands more often. 3 is basically the same thing, you just happen to do it while cleaning something else.
When you use soap you strip the natural oils from your skin. These oils help protect your skin from the environment, and hold in moisture. Losing that natural protection leads to drying and cracking of the skin.
It's very common for people that wash their hands a lot to develop cracked hands, especially around the fingertips (the finger tips see the most action). Mechanics and dish washers are good examples of occupations fraught with cracked hands. Maybe parents can go on the list?
The solution is to either limit the exposure of your hands to stop and water or apply something to your hands after the fact.
There are a variety of products out there to help with this. Incidentally, when my son was a new born I also had cracked hands (it was also winter). I personally used Eucerin Hand Cream. Whatever your brand, I recommend cream over lotion.
The cream helps not only to moisturize your chaffed hands, but to protect them from the elements in lieu of your stripped oils.
Petroleum jelly type ointments can also be effective, such as Aquaphor (made by the same company as Eucerin). Ointments can give you better protection than creams or lotions, but they're also much greasier and are thus more likely to leave a residue on objects they come in contact with. I prefer them for parts of the body that aren't likely to make much contact with anything else (elbows, cheeks, body). When I've had very cracked skin (right by the fingernails) I'll apply some of this thicker stuff, even though I inevitably leave residue on surfaces (and my glasses). Fingertips are constantly rubbing against objects(which you never notice until your finger is throbbing!), and the Aquaphor helps your finger to slide against surfaces instead of be abraded by them.
Instead of an ointment, you could use pure petroleum jelly, which is thicker and provides a stronger barrier against moisture. That is, it traps in your skin's moisture better, and it also repels environmental moisture that may wash away other more soluble substances. However, petroleum jelly doesn't have any medicinal properties and isn't absorbed by the skin. It's a purely protective solution. In the past, I have used petroleum jelly on top of other treatments, to help keep the medicinal creams from being washed/wiped away. Vaseline is the most famous brand of petroleum jelly, but since it's made of 100% petrolatum, it's easy to find generic substitutes.
There have also been times where my fingertips have been so cracked that I've had to apply some pain relieving antibiotic ointment with a band-aid. Sometimes the bandage is the best bet when trying to prevent further chaffing/irritation of the affected area.
Aquaphor and Eucerin are also both products recommended to us by our son's dermatologist. They're safe for baby skin, are not perfumed, and we use them on him for everything from diaper rash to eczema to dry skin. I'm sure comparable products of other brands out there exist, but I've not tried them so I can't give any personal recommendations. The downside of Eucerin/Aquaphor is that they tend to be more expensive than other moisturizers by volume. I pay the premium because lower-cost products either did not work for me us or made things worse.