Tile is a bad idea, IMHO. Too slippery to start and difficult to maintain if it gets cracked/damaged.

Look at overlays. Those can be installed quickly and the right kind can withstand those NY winters.

Overlay/resurfacing info

Thank you any suggestions on how to find someone that knows how to do overlays?

I'd look on the Internet. I have a lot of success with Google. Type in Concrete overlay and your zip code or town. You will learn about different types of overlays and also how to reword searches.

You could mortar bluestone on the flat surfaces (landings, treads) and thinset tile on the vertical surfaces (risers, etc).

Tiling flat surfaces in northern winter climates? There are tiles that can endure freeze/thaw climates (frostproof, etc) that also have a proper coefficient of friction rating for slippery-wet. But using them on surfaces like stair treads or stair landings that may need snow/ice chipped off of them? They can get dinged up during that process.