Stain is better, and TWP is the best. If sanding hasn't removed the paint, power washing won't do much, either. The nice thing about using an oil-based stain in a snowy climate is that it does make the wood impermeable to moisture, so it'll last longer. Hopefully. And on that note, you can leave it like it is & just wait 'til you have to replace the decking. You know, if it looks horrid. TWP makes a whole spectrum of stain colors, so you cd get dark. But then it'll burn your feet & the dog's feet, so there's that.

Do you have a power washer, or can you rent one for a day? Could help get rid of the rest of the paint. I've seen a number of decks done and the pros always went with a waterproof stain, and just coated the heck out of it, many applications, even where it snows. In time that residual paint will fade, or if not, may provide some funky washed out look. I'd go with a medium stain, unless dark is what you really want.

If someone complains about the projects we do at my house, I can always to tell them to look at it from the end of the driveway. It's about what you like or can live with.

stain is far more superior as paint coats, where stain absorbs it colors and protects

We have a deck that has previously been painted and can't quite get all the paint off. We sanded any everything. I hear deck paint is pretty terrible and peels a lot. Should we try a really dark stain? Or just tough it out and continue with paint, but which is the best in snow country?