The dangerous part of a snake is the head. This fundamental truth is the key to success in Slithereens. Any snake can chomp on any other snake's tail in the maze with impunity. When two snakes meet head-on, the longer one wins. To help you out a little, snakes that are shorter than you are pale.
Longer snakes are a deep, rich yellow.
Your only edge when you start is that you're noticably faster than the other snakes. A long snake is more dangerous from the front, but if you can avoid the head, extra length just means extra vulnerable area. It's an interesting balancing effect in the game. There are a couple of ways. The easiest way to grow is to eat the little animals that show up in the maze.