There is no doubt with the mail volume that obvious collector-request mail to places like Santa Claus is cancelled as it arrives and is held for dispatch until December 25. The integrity of the postmark date would dictate such.
We often judge finding a Jan 1, July 4, Dec 25 cancel by today's standards. Here are scans from the 1948 Postal Laws and Regulations showing that define holiday service - and show that post offices were open for limited service on Federal Holidays.
Limited window service:

No rural delivery:

Special Delivery still happened:
So finding non-philatelic Christmas postmarks is not uncommon if you keep your eyes open.