Even wearing gloves frequently, as most of us do pretty regularly at this time of year, will tend to dry out your hands more than you realize. Especially with the high quality of modern glove linings, that stuff just wicks out whatever moisture is in your hands – which is probably already reduced anyway because of the dryness of most ambient air.
The simple, easily tried and inexpensive (as well as healthful for other reasons, too) solution is to try to introduce some humidity to your surroundings. Simmer a pan of water on the stove (don’t let it run dry!) while you’re nearby; invest in a room humidifier; if you have a wood stove, as Lucky_Guy describes, just put a pan of water on top of that and keep refilling it. (In fact, if you have a wood stove or forced hot air heating, you’re already drying out the already-dry air even more.)
My uncle used to have an area humidifier that we’d fill every day with more than two gallons of water. Every day that thing was putting two gallons of air into the house air! And it was hardly noticeable, except that the slightly elevated humidity in winter will make a difference.