I wear gloves for some things but that's usually leather gloves to protect against blisters or bleeding when pruning, digging, using heavier tools, or working with wire. I've tried cotton gloves for light work but for anything that requires any dexterity they come off immediately. I hardly ever bother with them any more.
My problem is not so much the skin as the fingernails. When I'm playing in the dirt the fingernails break off, leaving sharp jagged blades that can cut and snag. Seems like I'm trimming some fingernails every day. I don't let them get that long to start with. I think the older I get the worse this problem becomes. If it bothered me enough I'd probably try something in my diet or even soak my fingernails in something regularly, but it's just something I live with. To me it's not a big deal, just a minor aggravation.
I don't mind getting dirt under my fingernails and cuticles all that much. I wash dishes in hot soapy water so my hands get clean. I don't wear gloves when washing dishes either, that should also lead to the hands drying out and cracking. I seldom have that problem. When I do, I rub a little hand lotion on them. The dry cracked hands are almost always in the winter when the weather is cooler and the humidity is low. It is humid here. Dew points below 70 F (21 C) are not considered that bad down here in the summer. I think that makes a difference, especially if you spend much time outside away from the air conditioning.
I think genetics has something to do with it too. My skin is naturally very oily. My wife was horrified when she learned that I wash my face with soap every day that I can. If I don't, even at my age I can wind up with blackheads and pimples, specially around the nose.
Phaedra, I don't have any suggestions for you. I imagine you are already using a hand lotion regularly. As much as you cook you have to have your hands in warm soapy water a lot unless you wear gloves when washing dishes. And you are talking about your fingertips, not your hands in general. Is there some activity where you are jamming your fingertips into dirt or some medium that might cause the dirt to get packed under your fingernails? Do you use a brush or certain cleaners to help get the dirt out from under your fingernails and cuticles?