I have a custom fence that works just fine without a texture pack on, however if any texture pack is put on the texture does not load (the fence uses a custom texture).

 

I get this error when a texture pack is put on

[16:04:31] [Client thread/WARN]: Unable to resolve texture due to upward reference: #side in minecraft:models/block/fence_nse

(for all fence models)

 

Here is one of my fence models

{
    "parent": "block/fence_ns",
    "textures": {
        "texture": "forge_theepicarnomod:blocks/AmboynaPlanks"
    }
}

Based on that error message, your fence model needs to define the texture that should be used for #side, not just #texture

 

Perhaps the texture pack models are different to the vanilla models

 

-TGG