I understand why these cards have "kneel all" text (to avoid drawing/standing more than 1 card).

What I'm not sure is: is this kneeling a cost? (and we know that you can pay cost only with own cards)

To make this short a simple question:

I have 1 "Bay of ice" in play. My opponent has no "Bay of ice". My opponent wins initiative. Does he kneel my "Bay of ice"?

Bay of Ice: "After a player wins initiative, that player kneels all cards named Bay of Ice, then draws a card."

Kingdom of Shadows: "After a player wins an I challenge, that player kneels all copies of Kingdom of Shadows to choose and stand a card with the S crest."

No, kneeling is not a cost. A cost will say something along the lines of "Do X to Do Y."

Kneeling cards the way these cards are phrased are part of the effect.

Actually, they do use the "do X to do Y" format. Kneeling the locations is indeed a cost. (e.g., that player kneels all copies of Bay of Ice to draw....)

However, note that these effects are passive. They happen whether you want them to or not. Further, the cards specifically say that the player that won initiative/an intrigue challenge does the kneeling. So since the card text specifically contradicts the rule that you can only pay costs with cards you control, any player can "pay the cost" of the passive ability. In the end, it is no different that Rhaegar Targaryen's text saying that any player may trigger the Response (when normally, you have to control a card in order to trigger its abilities).

So yeah, kneeling the location is a cost, but because the text says any player that meets the requirement can kneel the card to pay said cost, any player can. It really is more about making sure the effect only happens once per round (because if even one copy of Bay or Ice or Kingdom of Shadows in play is already knelt, the cost of "kneel all..." has not been paid).

Well ****... next time I'll actually read the card text before responding. ~ I mean it couldn't hurt right?