First of all, you do not need to install ANY ice on a remote server, but it is typically recommended.
Now, to get down to your question, each remote server has its own ice that protects it. Just like each of your main servers has its own individual ice that protects them (hand, deck and trash). This means at the beginning of the game, you have 3 separate areas that are vulnerable to attack, and you need 3 separate pieces of ice to protect all of them. Typically, hand and deck (or HQ and R&D) are the areas of primiary concern, and archives sometimes gets some attention later on in the game.
The fact that remote servers each need their individual ice makes it a bit of a challenge to create that one gnarly remote server that gets a ton of your ice, or to spread out your ice and create several remote servers.