In the books they are just regular horses, that was why the flooding of the river was useful, it removed the Black Riders' means of transportation. One would presume that in the movies they were the same.
The horses were killed in the flood, but not the riders:
'And is that the end of the Black Riders?' asked Frodo.'No,' said Gandalf.'Their horses must have perished, and without them they are crippled. But the Ringwraiths themselves cannot be so easily destroyed...
Three of the black horses had been found at once drowned in the flooded Ford. On the rocks of the rapids below it searchers discovered the bodies of five more, and also a long black cloak, slashed and tattered.
They were bred and trained to serve their masters, and were perhaps evil, but they were "regular" horses, not magical.