It could be more than dry skin. It could be a foot fungus. When you wear shoes without socks, moisture is not wicked off from your feet--this provides a warm, dark, moist environment, perfect for growing any number of foot fungi.
A symptom of foot fungus is both drying and cracking of the skin.
Even if you don't have a foot fungus yet, cracked skin creates a perfect place for a fungus to grow, so you need to care for it.
I would take no chances, get something like Lotrimen, Tinactin of any of the other foot fungus products that you can find in any pharmacy and start treating your feet and also spray in your shoes.
At least for the time being I would also start wearing socks, preferably white cotton socks. Natural fiber like cotton wicks off moisture better than synthetics and the undyed socks are better too.
Also, while wearing socks, make sure you change them daily.
Another good practice even after you clear up the problem is to make sure your feet get aired regularly and that you don't wear the same shoes everyday. Spray your shoes inside with antifungals from time to time as well to help prevent fungal growth in them.
Moisturizing your feet is not a bad Idea but its not enough.