Is there
such a thing as a tile or other product that can be laid over existing
concrete?

:You might also consider natural stone, such as precut (not split) slate,
using thinset portland cement to attach them to the steps. Make sure to
clean the concrete with brush and detergent, then etch with diluted muriatic
acid . This will assure a fast bond between tile or stone, and the
concrete. Slate and certain other stones and tiles provide a secure, rough
surface in the winter..