I have quite a few of custom armors, and all of them points to female imperial's foot texture

The problem being I'm not an imperial, I use custom race (Lattamer3) and form my understanding the armor will only take texture to which it is directed to, and for the skin case, female imperial. Will the game automatically redirect the custom armor's skin texture path to my custom race's or not?

Yes. The vanilla armours that show some skin also point to the Imperial texture as it seems to be used as a default. The object that uses this texture, however is set use any texture of a corresponding type of the race you use. No metter whether the race is vanilla or modded.

Following facts I found out the hard way and try to share whereever possible:

• Bodyparts in clothing items have to underly certain requirements to become actual bodyparts.
  
• For one the material must be "skin" (case-insensitive) or the game engine won't even bother and will use the textures assigned to the mesh in NifSkope as well as the material settings (bad thing for races and skin tint changes while in CharGen!).
  
• Then the "name" of the NiTriStrips/Shapes must start with a certain "keyword" telling the engine which texture slot of the race to use. The keywords I found out so far are (again all case-insensitive) "upperbody" or "arms" (which one is which gets vital for visability in 1st person), "lowerbody" (maybe also "legs"), "hand" and "feet". I think the race texture slots these direct to are self-explaining. There's also "tail" but so far it was of no real effect in my tests.

When these criteria are met, all material settings will be overridden by the game engine (for skin tint and color as defined in CharGen), which is also the cause for why there will never be glowmaps on bodyparts (the emissive value of the material is vital for glowmaps to work, but it's senseless to change this in the NIF files due to that), and the according skin textures of the race and the texture slot will be used, regardless of what's assigned in NifSkope.

• !Attention!: Although the game engine overrides this setting, the texture assigned in NifSkope is still used to check for the normalmap. If it's missing but not the actual race's one, you'll still get "missing normalmaps" error indicators (pitch-black or invisible mesh) ingame!
  
• Also I found out the hard way you can't simply assign "any" texture filename here, but it has to be in-line with the actual races' texture filenames and most likely also folders. "textures/characters/imperial/(fe)male/foot(fe)male.dds" is the least likely to go wrong and everybody has this file on the drive, so it's commonly used. "textures/characters/dragon/footmaledragon.dds" caused my dragon to become 50% translucent although there's neither in the textures nor the meshes anything causing that! (A quick rename of the file and the assignment into "footmale.dds" fixed it.)
  
• Last but not least there's also a "remark" character, the ":". This is used to tell the engine the keyword ends here, ignore what's coming afterwards. For example names like "foot:upperbody" are not uncommon in some female body mods I know. The engine will of course still use the foot slot texture and only the foot!

To follow on a little from Drake's response.

The vanilla body uses more textures than the replacers, which use less mainly to avoid seams. The single "foot" texture avoids the problems of matching the edges of one texture map to another because they are literally the same map, so that location can only have one shade of skin. The "head" and "hands" textures usually are separate, and so neck and wrist seams are the most common (Chokers and wristbands needed!)

That means that an armor needs to come in multiple versions to match the texture mapping of the body, with the vanilla version assigning the skin of the arms to "upperbody", and the HGEC/Exnems version assigning it to "foot:upperbody". (I don't recall if BAB and FF do the same) If you run the wrong combination, you get toes on your arms, or nipbles on your feet. IIRC all the custom races use the HGEC map assigments and have a "foot" texture for the whole body.

This is only a problem for playable outfits, an NPC-specific outfit can use any names it likes for the maps and assign specific textures in the nif file. I always avoid the use of "skin" as a texture name in these, even in situations where it would work OK, just to make it obvious if I accidentally put an outfit on the wrong character. I've also used custom bodies for NPC's (really a "nvde" outfit that has non-skin skin pointed to a custom texture) to make them immune to texture replacers.