It is possible to move on ice blocks while crouching, in a direction up to 45 degrees away from the direction you should be moving based on the movement key you are pressing.

How to replicate: (this is shown in the video "Ice Sneaking Direction Glitch Take 3")

1. Build a flat surface of ice blocks. Stand in the centre, and face diagonally on the X/Z axis.
2. Move your crosshair to be just to the side of the exact diagonal between the X and Z axis (it doesn't matter which side). Your crosshair should not move from this point onwards.
3. Wiggle your player left and right, alternating directions a few times each second.
4. While still wiggling, crouch.

If the glitch has happened, you will notice your direction of movement has changed. You can stop wiggling, but stay crouched. Now if you attempt to sneak left or right, you should notice that your character moves straight along either the Z or X axis. This can be made easier to see by doing either (or both) of the following;

• Switch to third person view. You should see your character's body (most noticeably their arms) shudders while you move during the glitch.
• Build a flat surface of non-ice blocks connected to your ice surface, at the same level. Once you have begun the glitch, if you sneak off the ice and onto the non-ice blocks, you will notice your direction of movement changes back to what it should be.