You're correct on the songs.
Eisenberg is not mentioned as vocalist/composer
'for' Nine Horses, he's only described as
'a' vocalist/composer, similar to how the descriptive words 'drummer' or 'ex-Japan' is used with Steve when he's mentioned in print.
I would doubt that he's the new guy in Nine Horses. Likely he's available for these engagements and it was an opportunity to debut new material, perhaps to test audience response, maybe they'e been thinking about touring.
With the lyrics on Snow Borne Sorrow being written by David, it would be a drastic change in style and content if another lyricist took his place. Might still be interesting and good, but it wouldn't be the same band.
I'm really interested in this solo project of Steve's. There've been many mentions of this, David especially saying he's been encouraging Steve to do it. I wouldn't be surprised if it was an intrumental album, but I'd like to hear Steve sing again, or even duet with David.