Slate with a natural split-face has a good mechanical coefficient of friction because of the rough surface.
With honed/polished slate, as with any other product that has a smooth surface, it’s a different story – it can get slippery when wet. New Dimensions Solutions, LLC produces an interesting sounding product called “Skid Safe”.
I do not have any personal experience with this product, but if the advantages are as good as claimed, it seems like it would be a tremendous safety addition. For further information, please have a look at their website: http://ndclean.com/skidsafe.html
If anyone has used this product, please leave a comment with your experience of its efficacy.