Since there is no HL2 Model Viewer, what program are you guys using to modify skins?

There is an HLMV for Source. Its in the Source SDK.

And you don't use HLMV to skin...

Allright.... there is no "program" to skin with.
a standard painting program will work (NOT MS Paint) like Photoshop, PSP, etc.

All textures are in the GCF file You extract them with this
http://nemesis.thewavelength.net/index.php?p=26

Textures all have a VTF extension. I edit the textures with Photoshop using this Photoshop extension
http://nemesis.thewavelength.net/index.php?c=154#p154

Apparently there is another way to open VTF files but I don't know what it is. Maybe someone else can help with that

Then you can view the model with the Source model viewer, located in the SDK menu. You will have to manually add DOD manually to the SDK using this guide
http://www.dayofdefeat.net/forums/showthread.php?s=&threadid=55943

There that's everything I know

VTFEdit is the companion program to the VTF plug-in and is more powerful and has more option. It can also do environment maps and animated textures.

http://nemesis.thewavelength.net/index.php?c=149#p149

I will say this as someone who used Paint Shop Pro for far too long, if you can get Photoshop, do so. Don't get me wrong I will always think fondly of PSP, but PS is just so much more powerful than I ever thought it could be.

Plus, nearly all videogame companies use Photoshop as far as I know.

Tehe, I switched from PSP 7 to PS recently. PS still annoys me sometimes (simple things are more complicated than in PSP) but when it comes to actually drawing skin details PSP (esp. version 7) is nothing more than a toy compared to PS.

Crash if you want to manipulate skins, go for PS and some good grunge brush sets. Or use Gimp (open source) if you can't get PS.

I use PSP 8.10 with the .VTF plugin - I also use VTF Edit, VTF Tool, & VTF explorer sometimes to view them aswell (when im too lazy to open PSP 8)