Podiatrist (NHS) here :
Get a footfile (one of the double sided emery ones) and dry file , using long swipes in one direction. If you have splits , go along the length of the split , not across them (you don't want to pull the skin about too much)
Put your foot over the loo or a bit of paper on the floor . It'll come out as a dust .
Then soak your feet , 10-15 minutes.
Rough dry (so leave them a bit damp)
Warm up some cream in your hands ( use a Urea based one - between 25-40% urea , like Flexitol ..other brands are available 
)
Put on cotton socks and let the cream absorb , the heat from the socks helps .
Do the cream Every Day and the filing every 2-3 days .
In a week you'll notice a difference , in a month you'll be amazed (skin takes 28 days to turn around)
If you go to have it scalpelled off , your heels might be tender after . I tend to use a single use file to off the dry skin, blade to reduce any fissures then file to finish , so as not to leave the heels too over done .
Then the file/cream/sock advice .
Your heel takes your entire bodyweight each time it hits the floor . The skin is the toughest on the body , but because of the fatty padding , not a rilliant blood supply.
Heel splits are a bugger and one of the reasons we see ulcers in clinic .
So prevention is key .