After Bran meets the three eyed raven in Game of Thrones, he shows him the past by warging into a weirwood tree. In the finale of season 6 when Bran and Meera almost reach Winterfell (Benjen Stark takes them there) he again wargs into the old weirwood tree and finds out that R+L=J. How does he do it? Can he see the past from any weirwood tree? Or just any ordinary tree for that matter...
Bran Stark is a warg and a greenseer, with unmatched ability. A greenseer is the name for the wise men of the children of the forest who had magical abilities that included power over nature and prophetic visions.
The weirwood tree is a species of deciduous trees found in Westeros, now found most commonly in the north and beyond the Wall.
Most weirwoods have faces carved into their trunks. This was done by the children of the forest in ancient days, and is now done by the free folk as well as other descendants of the First Men, such as followers of the old gods in the Seven Kingdoms praying to heart trees in godswoods.
Weirwoods are considered sacred to the followers of the old gods, and children of the forest believe weirwoods are the gods. The greenseers of the children of the forest can see through the eyes of weirwoods with carved faces. Since trees have no sense of time, the greenseer can see into the past or present when looking through the eyes of a tree. It is said that through the faces the old gods watch over the followers and bear witness to important events.
In his first vision he sees his late father Eddard Stark standing in the woods outside of Winterfell, through the weirwood roots. According to the Three-Eyed Raven, Bran can see what the trees see, but people cannot hear him; therefore, he cannot change the past. When Bran cries out to his father, all that is heard is a whisper on the wind (though it's later implied that he does, in fact, impart a message to Reek through the weirwood trees at Winterfell, which could prove that he's more powerful than the Three-Eyed Raven realized).
"Chaos is a Ladder"
When Bran quotes his own phrase to Petyr Baelish, he is recalling a conversation that took place between Baelish and Varys in an earlier season indoors in King's Landing.
This indicates to me that there is no tree requirement, weirwood or otherwise.