When a lot of cobblestone walls are used to fill a large cubical area the world will lag excessively, making building difficult.
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Cannot confirm.
See screenshot.

This ticket is invalid as it relates to a modded or 3rd party client/server.
Any non-standard client/server build needs to be taken up with the appropriate team, not Mojang.
Any plugin issues need to be addressed to the plugin creator.
This site is for addressing issues related to the base unmodded MineCraft.
I've only been on a single player instance and even the normal texture pack and client causes lag with fences and walls in the pattern.

Given the custom font, you're modded. Even if you change to a vanilla pack, you still have the mods installed that would support HD packs, your game is still changed.
I added screenshots with the newest snapshot showing the fps with and without the walls. The client is not modded, but the problem still persists when there are a lot of cobblestone walls stacked together, getting worse with a bigger stacking.
Yes I had mcpatcher installed and didn't realize this was a mod, sorry about that. However the problem still persists without any mods, the new (green)pictures use snapshot 13w04a, without mods.

Unable to reproduce it here.
No walls, 99FPS: http://s13.postimage.org/pwqaary6f/2013_01_28_17_01_08.png
5x5x5 Cube, 99FPS: http://s8.postimage.org/s8a10p20l/2013_01_28_17_01_19.png
Have you tried doing this on a superflat world to see if the drop is noticeable there? There's a couple potential reasons for this (texture changes, the sheer number of polygons rendered at once), but being able to reproduce it will let the devs figure out what's up.
Seeing your low fps I'd guess the change in entity counts is more likely to be responsible for your lag than the cobblestone fences.
If this happens on a superflat world please let us know.
It does, but it takes a riduculus amount of cobblestone walls to get me down to half fps on a superflat world. I added pictures. More like, I added cobblestone walls until I started "double-placing" them.

5x5x5 = 125 blocks.
10x10x5 = 500 blocks, and that's the point where my GPU's fan started spinning up, though still not bogged.
10x10x7 = 700 blocks, and that's when I was getting a bit of visual lag when placing (though not double-blocking yet).
10x10x10 = 1,000 blocks, and when placing those last 100 I finally started double-blocking...
Though the framerate when not changing blocks was unaffected.
http://s8.postimage.org/h34kjqp0l/2013_01_29_06_35_01.png
So this is a computer/rendering performance issue, you'll likely see the same thing with other models that have lots of visible surfaces even when grouped (like fences). Unlike other blocks (standard square ones) that mold and hide eachother when grouped (only the outside polygons existing for rendering), transparent blocks have surfaces that still require rendering even when "covered" by other transparent blocks.
My specs, for comparison...
CPU: Intel Core 2 Quad Q8400
GPU: Radeon HD 5770
RAM: 4GB
OS: Windows 7 Home Premium x64
Java: 1.7.0_11 (7 u11)
Unable to reproduce. I can see why this happens though, it loads 26 textures for each wall in the middle of it...