Does the Direction of a Huffman Tree Child Node Matter?

So, I'm on my quest about creating a Java implementation of Huffman's algorithm for compressing/decompressing files (as you might know, ever since Why create a Huffman tree per character instead of a Node?) for a school assignment.

I now have a better understanding of how is this thing supposed to work. Wikipedia has a great-looking algorithm here that seemed to make my life way easier. Taken from http://en.wikipedia.org/wiki/Huffman_coding:

• Create a leaf node for each symbol and add it to the priority queue.
• While there is more than one node in the queue:
  • Remove the two nodes of highest priority (lowest probability) from the queue
  • Create a new internal node with these two nodes as children and with probability equal to the sum of the two nodes' probabilities.
  • Add the new node to the queue.
• The remaining node is the root node and the tree is complete.

It looks simple and great. However, it left me wondering: when I "merge" two nodes (make them children of a new internal node), does it even matter what direction (left or right) will each node be afterwards?

I still don't fully understand Huffman coding, and I'm not very sure if there is a criteria used to tell whether a node should go to the right or to the left. I assumed that, perhaps the highest-frequency node would go to the right, but I've seen some Huffman trees in the web that don't seem to follow such criteria.

For instance, Wikipedia's example image http://upload.wikimedia.org/wikipedia/commons/thumb/8/82/Huffman_tree_2.svg/625px-Huffman_tree_2.svg.png seems to put the highest ones to the right. But other images like this one http://thalia.spec.gmu.edu/~pparis/classes/notes_101/img25.gif has them all to the left. However, they're never mixed up in the same image (some to the right and others to the left).

So, does it matter? Why?