Why not? (Alternately you can use the sub-term 'Scaly'.)

"Furry" is an umbrella term catch all for anthropomorphic animal characters. Some people like to make a hard distinction from more specific fandoms and communities, and some people like to have an even broader view and lump things like fae creatures in with it. Just have fun and call yourself whatever feels right to you!

Given the difficulty of building and wearing a snake suit, I would say it makes them especially furry.

If they want to be a furry, that makes them a furry. Lots of furs don't own fursuits of any kind (they're expensive and require a lot of maintenance).

Yup, cause furry is for anthropomorphic animals, not just fluffy anthro

I mean technically a scalie but still under the furry umbrella