Both approaches are valid, tho the resulting flexibility of usage is different.
Vector Graphic approach
You can use any vector design software to create a Enhanced Metafile (EMF). I would use Inkscape, but Adobe Illustrator and Corel Draw are able to create this files too. Remember to transform any Fonts in Outlines.
To use the emf file as a Marker Symbol, you need to choose Picture Marker Symbol Type in the Symbol Properties, and to browse the emf file.
Pros: Very simple processing;
Cons: You can not change the symbol colors in ArcMap, for that you need to create a new emf symbol.
Vector Graphic approach
Using Inkscape and the Online Font Converter you can follow this tutorial made by cleversomeday blog to produce a set of Fonts to use in ArcMap to create simple or composed marker symbols.
After installed In your computer you can use it as character marker symbol type.
If you need to create composed symbols, take special care with the size and alignment of the several fonts, so once in Arcmap they correctly overlap in ArcMap.
Pros: You can reuse the same symbol (font) with different color without changing the original file, making it more suitable to use in composed symbols;
Cons: It's a more complicated and time consuming process. It's difficult to create symbols with many different colors (ou need to create one font character per color)
How to decide what approach to use?
It depends of your needs and available time. If you are in a hurry to create a fast symbol or you know that you wont need any color variations from it, go for the EMF creation (Try to keep all your emf files in one folder, or you can very easily forget where is the original EMF file that you use in a certain project).
If in the other hand, If you have time and want to create a set of custom symbols to use in composed symbols, in many different projects and with infinite color and order combinations, you should go for the font creation.
A possible reason for this may be that the features have been converted to graphics. This will show the points, but will not allow editing. Can you select the points using the Select Elements arrow?
![Select Elements](https://i.stack.imgur.com/TmNgE.jpg)
If so, these points are graphics. You can remove them or turn them off in the Annotation Groups tab. Right click on your data frame in the table of contents (called Layers in your example). Select Properties and go to the Annotation Groups tab. If there is an annotation group, you can remove it or turn it off.
![Annotation Groups](https://i.stack.imgur.com/hVKm5.jpg)
Note, the above screen capture is from ArcGIS 10.0. I'm not sure if it's different in 9.3.
Best Answer
To add to the other great answer![enter image description here](https://i.stack.imgur.com/YPEsj.jpg)
This is the way to do it with font symbol (in this case I find a hiker symbol in the ''ESRI NPS 9.1'' font)
notice the lock symbol next to the layer (bottom left white box), the hiker symbol is locked so it will stay black, the circle symbol under is left unlock so you will be able to change the color
During arcgis installation you should get a lot of font (with name beginning by ESRI) with all kind of symbol