If this model that you are trying to export as a mod didn't have proper textures to start off with then they won't appear in the mod viewer because basically they don't exist outside of max -just as DarkMatrix said.
However if the model did have textures to begin with and they are not appearing in the mod viewer after exporting then it could be that the texture files are of irregular dimensions or of an unsupported format.
I've come across models that use a mixture of texture formats before. The modviewer will only show .bmps.
People have posted on the subject of texture dimensions before. Basically any that is a multiple of two should show up but it is best to keep to 16, 32, 64, 128, 256, 512, and 1024 sized bitmaps (note they don't have to be square).
So to summarise (and I'm no expert)...If the original model didn't have proper textures - then you most definitely won't be able to see them in the modviewer.
If the textures are of the wrong dimensions, then they will need to be adjusted.
if the textures are in anything other than bmp format, they won't show up in the modviewer either. You need to convert them.
On the subject of applying textures, basically select al of the objects and press M.
Click on the arrow on the left of the box below the texture palette.
A new dialog should open, select scene from the options. Now a list of the textures that are available for this scene should appear. By double clicking each one you should be able to set the bitmaps used for the various effect channels (diffuse, self illumination, etc). This is all dependent on there already being UVW coordinates present, otherwise you would have to map everything yourself. You might wanna get someone else to do that for you if you do not know how.