Como JK mencionou, The Last Jedi diz muito pouco sobre Snoke. Mas as coisas que aprendemos são:
Snoke commands the First Order from his massive command ship. It is instantly recognizable to members of the Resistance.
Se ele governa de qualquer planeta em particular, não há indícios sobre o que é.
Além disso, o Snoke é
an extremely powerful Force user. He effortlessly suspends Rey in the air and drags her from place to place in his chamber. Most impressively, he drags General Hux across a floor from perhaps many parsecs away, during holographic communication.
Ele também
reads the thoughts and emotions of Rey and Kylo with ease and bridges their minds across a vast gulf of space.
Também aprendemos que
Snoke first influenced Ben Solo to join the Dark Side during the latter's training under Luke's tutelage. This may also have occurred across a great distance.
Além disso, descobrimos que
Snoke employs a squad of eight Praetorian guards (clad completely in red). Previously, Palpatine also had Praetorian guards in his service.
Do diálogo entre Snoke e Kylo Ren, aprendemos que
Snoke is quite preoccupied with nurturing the "next Vader" and is deeply disappointed by Ren's inability to rise to this challenge.
Finalmente, talvez a coisa mais interessante que aprendemos:
"As detailed in the [film's] Visual Dictionary, Snoke wears a ring with an obsidian setting from the catacombs beneath Darth Vader's castle on Mustafar. But the truly interesting tidbit is that the gold ring is etched with glyphs of the Dwartii, presumably a reference to the Four Sages who served as controversial lawgivers and philosophers from the dawn of the Galactic Republic."
( Fonte )
Este último ponto pode sugerir algo sobre as origens ou motivações de Snoke - embora nada seja certo.