During Diplomatic Immunity my Sneak skill stopped being effective

Sneaking is complicated. The following factors are considered:

• Visibility
  • Line of sight
  • Invisibility (completely eliminates visibility penalty)
  • Light level
• Noise
  • Movement (doubled for running)
    • Weight of armor
    • Muffle (halves or eliminates movement penalty)
  • Actions such as swinging a weapon (except all daggers) or casting a spell (except with the quiet casting perk)
  • Line of sight
• Distance (falls off quadratically, detection cuts off outright at 2500 units)
• Enemy skill level minus your sneak skill.
• If in sneak mode, the Stealth perk bonus (detection is always active; you can be undetected even if you're not sneaking at all).

The weather is not on this list. Enemies can detect you just as easily in a blizzard as they could on a calm, overcast day (or night). Also, light level has an extremely large effect at the extremes (i.e. in very bright or very dim light), so bright sunlight is not an ideal test condition because you are likely to be detected as soon as you cross the 2500 unit distance threshold, even at very high skill levels. I recommend picking a dimmer location with more reproducible light levels, such as the main hall in Dragonsreach. You can then test detection against Balgruuf or whoever else is in the room, by just looking at the sneak indicator.

A couple of additional things to note about light:

• Skyrim doesn't know or care about mods that change how light is rendered (e.g. most ENBs). It does know and care about mods that add or remove lightbulbs (e.g. Relighting Skyrim).
• It may not look like it, but sunlight is far brighter than the brightest parts of most dungeons.