Krampus would I think have issues with thresholds, Kringle has a dispensation from the White God, given at his annual St Nicholas day lunch with Uriel (who ALWAYS orders the Angel food cake, with Sunny Delight as his beverage).
Krampusnacht is supposed to be 5th December the eve of the feast of St Nicholas which is why we never saw Krampus during Christmas Eve or The Good People. He had his day a couple of weeks before.
Given the fact we never see Kringle and Krampus together, and that Odin has assumed many, many forms it isn’t impossible that Odin is in fact Krampus, a sort of Jekyll and Hyde arrangement. Kringles membership of the Wild Hunt would kind of support it, it’s more of a Krampus like behaviour than a Kringle.
Suppose the original Mantle was Kringle and Krampus BUT belief in the former enhanced that part of the Mantle changing its nature whilst the Krampus element dwindled but could never be eliminated. Krampus would be at his strongest on the 5th December and Kringle his weakest.Kringle becomes his strongest on the 6th December when Krampus gets chained down by Uriel, and Uriel gives Kringle his pass, making sure Kringle is dominant within the Mantle. A bit like the power duality between the Winter and Summer Queens. That would be consistent with the mythology.
If so Krampus isn’t in Demonreach and a battle between the two unlikely, but a story set on the 5th and 6th December featuring Kringle/Krampus and Uriel would be fascinating.
