I, like many, have had some issues with the distribution of the Westeros cards, that have caused some of my games to be much less fun and more frustrating than I would like. I think I may have found a general solution that modifies some of the ideas already given to fix this. It sounds more complex than it is in practice:

Deck 1: Temporarily take out Winter is coming and separate what's left into two sub-decks. a)2 Mustering, 2 Supply, and 1 Last Days of Summer. b) 2 Mustering, and 2 Supply.
Shuffle both. Randomly take one card from from the 2nd sub-deck and add it to the first. Add Winter is coming back to the second sub-deck and re-shuffle. Finally, place sub-deck a (which now has 6 cards), and place it on top of sub-deck b.

Deck 2: Do the exact same thing as Deck 1, just using the Game of Thrones, and Clash of Kings in place of Mustering and Supply.

Deck 3: No change.

I think that this has several advantages. Firstly it allows for re-shuffling, but at the earliest, it will happen in the 7th turn (on average it will occur in the 8th or 9th). Secondly it keeps a bit of the 'Unknown' factor, as you have no idea whether it is Mustering or Supply that is 3 of the six cards. If there is still not enough uncertainty to suit your taste, simply include Winter is coming as a possibly card to pull from the 2nd deck when you add one to the first.

Played this last night, and it worked like a charm.

Oh, and another house rule we use, is that the Wildling Attacks card acts like the Winter is coming card if the Wildlings would attack at 0 strength AND no battle cards have been expended. As there is nothing to gain for anyone.

Sorry for the size, and I hope it all makes sense. But let me know what you think in either case. :0