With Summer's death, only two Stark direwolves are still alive: Nymeria (Arya's) and Ghost (Jon's). Jon is the only one still in possession of his, as Arya set Nymeria loose to spare her from being put down after biting Joffrey.
The origin of Hodor's simple-minded nature and inability to say anything other than his own name had been the subject of much fan speculation, until it was revealed in this episode. Shortly thereafter, it turned out that a user on a forum dedicated to the books had correctly guessed that 'Hodor' was short for 'Hold the door!' back in 2008 (three years before the series even started). He was incorrect about the origin of the phrase, though.
HBO's viewers guide confirmed that the man the Children of the Forest impale with a piece of obsidian, creating the first White Walker, is the Night King. Vladimir 'Furdo' Furdik plays both incarnations in season 6, taking over the role from Richard Brake who played the role in seasons 4 and 5 (Furdik was a stunt performer on the show since season 5). Also note that the spiral pattern of monoliths around the weirwood tree matches the spirals made of dead horse parts created by the White Walkers in Walk of Punishment (2013). The arrowhead mountain seen in the background is seen again in Dragonstone (2017).
Note that one of the Children kills a wight with a dragonglass spear, the same kind that Meera uses to kill a White Walker moments later. This implies that dragonglass can kill both wights and Walkers. In the books published up to this episode, Sam finds out that dragonglass instantly kills the Others (as White Walkers are called in the novels), but has barely an effect on wights (it is so brittle that it breaks); wights are only extremely susceptible to fire. When he tells Melisandre, she states that "Necromancy animates these wights, yet they are still only dead flesh. Steel and fire will serve for them. The ones you call the Others are something more." The showrunners have confirmed that they purposely changed this in the series because they lacked the resources to set every wight performer on fire. On the show, the wight seem to share this vulnerability to fire, given that the Night King can walk through fire unharmed, yet the wights dare not come near.
While the series has killed off numerous characters who are still alive in the novels, most have not been confirmed as either future novel plot points or inventions of the showrunners. However, Hodor is the second major character, after Shireen, who author George R.R. Martin confirmed will die in a future novel in a similar manner to the series. Showrunners David Benioff and D.B. Weiss have stated that among Martin's future plot elements in the novels, this was the second of three "Holy sh!t!" moments (Shireen was the first). He verbally described it to them in a hotel room meeting, and of all revelations, this one gave them the biggest emotional punch and left them the most deeply shaken.