Yes, you can assign a completely different texture to the fence by editing the model files (assets/minecraft/models/block/oak_fence_*). You can find more info on creating and editing models in this tutorial. Judging by your request, all you need to do is to change the texture variables so they are different for the top and side faces, then make the appropriate textures.
I can't make wood planks and fence be cool same time.
I want to use both vertical and horizontal lines (to split planks) in wood planks texture, but as a result of that i got ugly unnatural fences.
Is any way to control fence texture? May be control the way how it wraps?
Putting the CENDENT back in transcendent!