Since First Snow of Winter takes effect after the first challenge of the round is initiated, can I as the first player initiate a military challenge and then cancel the effect with borderland keep? I understand this is type of thing is typically abnormal but since the effect takes place "during" a military challenge I was hoping it might work...

Borderland Keep can only cancel triggered effects. First Snow is a passive effect that happens whether you want it to or not. So Borderland Keep is not a legal cancel against the plot, military challenge or not.

But Forgotten Plans will cancel it right?

Technically no. Forgotten Plans will not "cancel" anything since it is a blanking effect, not a cancel effect.

But Forgotten Plans will blank First Snow during the Challenge phase so that its effect never happens in the first place.

Thanks Ktom. I've been trying to think about how I'm going to deal with this card. Got a feeling it's gonna royally screw me at some point...

Bran yourself into a Forgotten Plans.

Good call