If two archetypes modify, alter, replace, or otherwise touch the same class feature they are not, by a strict interpretation of the rules, compatible.
From the Advanced Players Guide:
A character can take more than one archetype and garner additional alternate class features, but none of the alternate class features can replace or alter the same class feature from the core class as another alternate class feature.
Individual GMs, in cases where it would make sense for a the two modifications to stack who think it's not too cheesy, might make an exception for you if you ask nicely.
Not allowed by RAW.
A character can take more than one archetype and garner additional alternate class features, but none of the alternate class features can replace or alter the same class feature from the core class as another alternate class feature.
The FAQ on Archetype Stacking gives more leeway for archetype stacking.
Archetype Stacking and Altering: What exactly counts as altering a class feature for the purpose of stacking archetypes?
In general, if a class feature grants multiple subfeatures, it’s OK to take two archetypes that only change two separate subfeatures. This includes two bard archetypes that alter or replace different bardic performances (even though bardic performance is technically a single class feature) or two fighter archetypes that replace the weapon training gained at different levels (sometimes referred to as “weapon training I, II, III, or IV”) even though those all fall under the class feature weapon training. However, if something alters the way the parent class feature works, such as a mime archetype that makes all bardic performances completely silent, with only visual components instead of auditory, you can’t take that archetype with an archetype that alters or replaces any of the sub-features. This even applies for something as small as adding 1 extra round of bardic performance each day, adding an additional bonus feat to the list of bonus feats you can select, or adding an additional class skill to the class. As always, individual GMs should feel free to houserule to allow small overlaps on a case by case basis, but the underlying rule exists due to the unpredictability of combining these changes.
so the question is do these two archetypes stack? or do they not because both archetypes touch on the familiar class feature. one by restricting what you can choose as a familiar and the other by removing the archetype.
One archetype weakens a class ability and the other removes it altogether. If both archetypes are balanced, so that each weakened ability is matched with a strengthened ability and each removed ability is matched with an added ability, then applying both archetypes would result in a combined archetype that is stronger, due to a strengthen ability no longer matched by a weakened ability. Even the lenient FAQ version does not necessarily allow this stacking.
But the winter witch's restriction to cold-based familiars is a trivial weakening, probably exists mostly for regional flavor, so the combination won't be too unbalanced. The FAQ give the final decision to the GM.