Holidays are actually one of the best times to be making changes as traffic is significantly lower, and IMO, one should be aiming for an infrastructure where you can always ship changes without being afraid of the ramifications.

Architecturally that may mean many things - hitting "SHIP IT!" might push code into a staging environment for some final testing before delivering it onto a platter in production. Should you have multiple sites, it might involve rolling out the new stuff to just one of them until you see how it goes. Maybe you have feature flags and want to introduce a new change to all servers, but just 1% of the user population?

Fundamentally hitting "SHIP IT!" should be doing just that. Any constraints you put on how fast it gets to 100% of the user population are a risk control, and you need to optimize for a balance of developer happiness and system stability.

When you concede "We can't make changes because we're frozen" outside of a critical systems ('life critical') environment, you should quit your IT job and go become a fisherman or something.