More like an associate of Winter or with Winter, I doubt that Kringle would take a direct order from Mab for example, or that she would give one.. I think they actually agree on a lot of stuff, I also think because of his multiple mantles that he is way too complex to be a subject.
Yes, Odin & Mab agree on lots of stuff (as we saw in Skin Game)... though not on all things.
But the Kringlemantle is one of Winters/Mab's. Within the scope of Kringle's duties, it is
entirely subject to Winterlaw. Now... Mab does not wish to be seriously at odds with Odin, so she isn't likely to give
any orders that Odin -- or Vadderung -- finds deeply offensive. By the same token, Odin doesn't want to be seriously at odds with Mab, so Kringle is always looking for ways to be inoffensive.
When push comes to shove (if Mab orders something he's unwilling to do) Odin can simply take off the Kringlemantle and say, "nope."
The thing is:
neither of them want this to happen simply as a result of Aesir/Faerie political squabbling, or points of pride between the two monarchs or their courts. The Kringlemantle
and what it represents and does is important to both of them. Without ever actually speaking about it, they are lowkey collaborating to avoid needless conflicts; and both of them are pretty damned good at that sort of tactico-strategic thinking, so it works well (and has for hundreds of years).