So does Sasuke get wood style now?

[HyuugaHeir]

Nah, kabuto's just using hashirama's cell to utilise his medical ninjutsu to heal sasuke.

Sasuke's charcter would be ruin if he gains rinnegan or mokuton

 

[Shinato]

Pfff, no. Obito didn't get Rinnegan because he's not old. Zetsu confirmed this when he was heading to Rin+Kakashi.
You definitely need to be old to get Rinnegan.

Panel where it confirms that you need to be old to awaken it. Because if Zetsu confirmed it then he must have said something like:

"You'll have to be very old in order to awaken the Rinnegan."

 

[Almighty Ra]

I highly doubt Sasuke will get wood style..Obito had that ability due to the Zetsu attached to his half of his body. Sasuke is being healed and if Hashirama's cells are being infused in his body it's to awaken another Doujutsu or the over used Rinnegan.