It's very difficult to answer this without spoiling a little bit of the series. I have no idea where you are in the series, so I'll spoiler this block:
Walt is "special".
Officially, we don't know why. Damon Lindelof, co-creator of Lost, was asked it at Comic-Con 2011 and said:
One mystery that they said was always meant to be unexplained was the source of Walt's powers, which Lindelof likened to Stephen King's "Carrie," where it's just accepted without explanation that Carrie is telekinetic. "That's one of those things that never felt like a mystery to us: why is Walt special?" he said. "The answer is, because he is."
There are many fan theories on this, which can be found here. However, among them are the following:
Walt has some level of psychic powers. For example, In the episode "Special" (Season 1) while playing backgammon with Hurley, Walt thinks a number out loud and then rolls it. Also, when Locke is teaching Walt how to throw knives, Locke says, "Imagine it in your mind's eye." When he does, Walt is right on target. When studying native Australian birds, Walt tries to get his distracted stepfather's attention to look at the bronze cuckoo and when he can't a bronze cuckoo flies into the back door and kills itself. Finally, as you mention, Walt is chased through the jungle by a polar bear after reading a comic book with a polar bear in it.
Now, there are some counter arguments against this:
We later discover the Dharma Initiative were performing experiments with polar bears, as was evidenced by a comment made when Sawyer figures out how to get a fish biscuit. It can probably be assumed that the polar bears were being trained to turn the FDW to move the island, so that no human inhabitants had to be transported off-island. Therefore, this would explain their presence and suggest Walt had nothing to do with it.
So, none of this is conclusive. A lot depends on what theories around Walt you choose to believe.