jOLYON, the appearance of the Adobe logo next to any ".ged" file means that you have assigned Adobe as the program that you want the PC to use to open the file. You may have done this intentionally or not. It would be normal to use Notepad to open a simple text file (just letters and digits), which is what a GEDCOM or ".ged" file is.
However, if you are trying to import the file into a FH program, it won't matter what you have specified as the preferred program, as, by using an FH program to import it, you are over-riding that setting.
Going back to your initial question, it doesn't MATTER what you specify as the default program for opening a GEDCOM file, but specifying your own choice will help, but ONLY if you want to open it and examine it. Normally, there is no real reason to open one to read it yourself. Usually you want an application to open it, interpret it, and process it. Unless one is an expert in GEDCOM file syntax, one would not want to read it personally.
If this still isn't clear, perhaps someone else will explain it from a slightly different angle. If ever I can't understand a concept, getting an alternative explanation usually helps.
UPDATE a moment later, as Gadget says, "I'm not sure what your problem is now ". I don't actually think you have one.
Martin