Your character automatically starts with 50% worse shout cooldown, effectively making your beginning shout cooldown 50% higher than what is listed.
Player shout cooldown overtime can be decreased by a decent amount by learning shouts from word walls and also unlocking the shouts using dragon souls.
Player shout cooldown reduction is capped at 135%. You can check your shout cool down in game by using console "player.getav shoutrecoverymult" at start of game it is 1.5 and at cap it is 0.15, you can bypass the cap via wearing Greybeard robes.
Shouts now properly affect wards. You'll need higher tier wards to protect yourself against strong attacks. No more flicking a novice ward on your heavy armor warrior versus that dragon! This also goes for harmful player shouts also. Some other effects now also properly effect wards, for example spider venom
Nord - 12%
Lovers Stone - 15%
Talos' Scaling Blessing - 10%-25% (Acquire 1-25 dragon souls, through any means)
Speech Perk - 10%
Gift of Gab (Bard's College) - 5%
Talos Amulet - 4% (doubled if worshipper, quadrupled if Champion)
Greybeard Robes - 30% (all 3 pieces) - full set of Greybeard robes can surpass shout CD cap completely, each piece essentially lowers cap by 5%
Ancient Nord Armor - 4% (per piece) - full set grants bonus 4% shout cd reduction - total of 20%
Crown of Tongues - 9%
Corrupted Psiijic Robes - 5%
Ahzidal Full Set - 16% total
Dragon Aspect Shout (3 words) - 5%
Nord Neck - 6%, 9% for bloody variant (bosmer only)
Derived Attributes:
Words of Power Learned ~11% max
Words of Power Unlocked ~25% max
Important takeaway from this: if you want to have shout cooldowns at 0, you'll need to be wearing the greybeard robes with all of the non-equipment bonuses listed above.