I just spent a few hours of my time making a 1.6 compatible version of this texture pack. It is a mix of Vattic's and Affinite's textures, and all of the textures should work, however, the horse armor item and some of the horses are not HD. As well, I created a second version that has much calmer weather and minecart sounds. The instructions are included in the zip file, and I will put them in this post farther down.
I also included a 1.5.2 compatible version, which includes many of Vattic's textures.
To use this resource pack, you NEED to be running the 13w24a snapshot or later. I will not be explaining how to find or install these snapshots, as there are plenty of Youtube videos explaining this already.
1. Unzip the ZIP file containing the pack.
2. Copy the folder titled "[64x][1.6.x] Affinite's Faithful" or "[64x][1.6.x] Affinite's Faithful + Better Rain" that was contained in the ZIP file.
3. Find your resourcepacks folder, in the .minecraft folder. There are two ways to do this:
1. Open the latest snapshot of Minecraft. After logging in and reaching the main menu, click the "Options" button.
2. In the Options menu, there will be a button titled "Resource Packs."
3. Click it, and you will see a list of resource packs you have installed.
4. To the bottom left side of the screen, you should see a button titled "Open Resource Pack folder".
5. When you click that, it will take you to the folder containing your resource packs.
Method 2: (For Windows)
1. Go to your start menu, and in the search bar, type %APPDATA%.
2. A folder titled "Roaming" should appear. Open it.
3. One of the first results should be a folder called ".minecraft" Open it, again.
4. After opening your .minecraft folder, look for a folder titled "resourcepacks". Open it.
4. After having opened your resourcepacks folder, paste the resourcepack into it.
5. Finally, open minecraft, navigate to the resource packs menu item (See method 1 above), and select the resource pack you wish to use.
Note: There appears to be a bug that messes up the text when you close Minecraft with the Resource pack applied. On reopening minecraft, the text is unreadable. To fix this, switch back to the default resource pack, restart minecraft, and reselect the HD resource pack.
Finally, a disclaimer: All of the 64x64 textures included in this pack belong to Affinite, and are his intellectual property. All of the 32x32 textures belong to Vattic, and are his intellectual property. The modified sounds in this pack were downloaded from free sound fx websites found on the internet, and were edited by me, Benny_McRyan, into the Better Rain version of the resource pack.