Matt,
If you use a thinset, I would lean towards a latex thinset, just make sure what you buy is OK for exterior use. I suppose the Portland mortar would be OK, but I would rather epoxy this right to the concrete with a flowing epoxy. It would strengthen the crumbly concrete as it soaked into it plus it would permanently adhere the treads to the concrete substrate,
Epoxy is cool with being frozen and heated unless you get over 300 degrees Fahrenheit, in which case we have bigger problems. For this application I like the allstone the best. Here is the link:
http://www.defusco.com/glues-epoxy-polyester-etc-epoxies-c-82_500.htmlGlad to be of service,
Mark