It's the beginning of the plot phase and Bay of Ice is in play. My opponent and I both choose plots and reveal them. My opponent has a higher initiative count than I do and is going to win initiative. I play Ahead of the Tide to cancel the initiative count and win initiative instead. My question really has to do with the frame action window and when effects resolve.

This is how I see it:

Initiative is counted in part II of the frame action window. I'm assuming that the winner of initiative is determined at the very end of part II. Ahead of the Tide is played during part II, but before the actual determination of winner takes place. So even though Bay of Ice is a constant effect and my opponent was going to win initiative, he or she would not kneel Bay of Ice to draw a card as he or she never actually won initiative.

Is my interpretation correct? Thanks for the help.

Well, you have the right overall answer, but I think your reasoning through the Framework Action Window might be a little off. Let me go through it the long way so that you see, in detail, how that window - and situation - will work out:

Step 1.1: Initiate first framework event : Players Choose and Reveal Plots
Step 2.1: Save/Cancel opportunity to players choosing/revealing plots
Step 3.1: Resolve choosing/revealing plots (chosen plot cards are officially the players' revealed plots; constant plot effects active)
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Step 1.2: Initiate second framework event: Initiative is Counted
Step 2.2: Save/Cancel opportunity against Initiative Count (Ahead of the Tide can pretty much only be played here)
Step 3.2: Resolve Initiative count (high initiative - or person who played Ahead of the Tide - is considered winner of initiative count)
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Step 1.3: Initiate third framework event: Winner of initiative count appoints First Player
Step 2.3: Save/Cancel opportunity against determination of First Player
Step 3.3: Resolve determination of First Player (named player officially becomes First Player)
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Step 1.4: Initiate fourth framework event: Execute "When Revealed" plot effects
Step 2.4: Save/Cancel opportunity against "When Revealed" execution
Step 3.4: Resolve "When Revealed" execution (according to the FAQ, these are actually treated as passive effects and are resolved in Step 4 of the action window, so this framework event is more of a reminder than a set of Steps 1-3)
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Step 4: Passive effects - to anything in Step 1.1 - Step 3.3 (and where Steps 1.4-3.4 actually happen): NOTE: Resolution of "When Revealed" plots must happen before any other passive effect.
Step 4.Ia (ie, Step 1.4): Initiate first "When Revealed" plot effect (as chosen by First Player)
Step 4.IIa (ie, Step 2.4): Save/cancel opportunity against first "When Revealed" plot effect
Step 4.IIIa (ie, Step 3.4): Resolve first "When Revealed" plot effect
Step 4.IVa: Passives activated by resolution of first "When Revealed" plot effect can now be legally included in resolution of passives.
Repeat Steps 4.Ia - 4.IVa as necessary for all "When Revealed" plots
Step 4.Ib: Initiate other Passive effects - in this case, Bay of Ice: Winner of Initiative - as determined in Step 3.2 - kneels all copies of the location in play
Step 4.IIb: Save/cancel opportunity to Bay of Ice's effect
Step 4.IIIb: Resolve Passive - Bay of Ice: Winner of Initiative draws a card
Step 4.IVb: Passives activated by the resolution of Bay of Ice can now be legally included in resolution of passives
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Step 5: Response effects (to anything in Step 1.1 - Step 4.IVb)
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Step 6: End Window (all moribund cards physically leave play)

A bit of a mouthful sure. And the short answer really is "because Ahead of the Tide is a cancel effect, it takes place before the opponent who 'would have won initiative' ever actually and officially does become the winner of initiative." The implication, of course, is that Bay of Ice works for the person who played the event and not for the person with the highest initiative count. But it is important to understand the timing of the framework windows, where the cancel happens, and where the passive effect of something like Bay of Ice takes place so that the answer can be applied to other, similar situations.

Thanks for the very detailed response, ktom. Slowly but surely I'm getting a more complete understanding of how action sequences resolve. This really helped. Thanks again!