If it's so loose that you can peel it off with your finger nails, then a SHARP paint scraper should make the job go quickly and easily.
If it wuz me, I'd scrape the old paint off, sand down any grey weathered wood until you get clean solid wood, prime with an EXTERIOR ALKYD primer and top coat with an EXTERIOR ALKYD paint.
Also, considering these are steps, they could be slippery when wet. You need to add traction grit to your paint to ensure they're not. If it wuz me, I would give the whole set of stairs two coats of paint, and then apply another coat with traction grit to the tops of the steps only. Apply the first coat of paint within 24 hours of priming, and each coat of paint within 24 hours of the preceding coat (for good inter-coat crosslinking). Apply earlier if the previous coat is dry enough.
(I've never used traction grit, so you'll have to get advice on how to use the stuff from someone else. I THINK you just scatter it into the paint when it's still wet. Sherwin Williams stores sell a traction grit called "Shark Bite", so if you can phone up any Sherwin Williams store, someone there should be able to tell you how to use traction grit with paint.)