So...
the card does say it must contain the word "Summer" or "Winter"... so I would assume a card like Shireen Baratheon would not count since the "summer" in the flavor text isn't capitalized. So unless the flavor text starts with Summer or Winter, it's pretty unlikely. I haven't seen any artists with Summer or Winter for names either, so I guess we are good there. So basically the only non-seasonal cards you can get are:
Shores of the Summer Sea (AToTT)
Summer (LoW)
Summer Sea (Core, PotS, QoD)
Summer Sea Corsair (RotK)
Winter Cache (WotN)
Doesn't seem that game breaking, and I doubt if you are running that event any of these are really worth blowing the event for.