How do I exclude a single day from/preemptively snooze a daily alarm?
Apple's clock app isn't very deep - it mimics late 20th century watches in functionality, it seems. There is certainly no problem with that as it serves most people's needs completely and many users needs to varying levels. 

In this case, I suggest that you look beyond the app. If you only want to use that app, you will need a system like what you do know - remind yourself later, or rig a complex pattern of alarms (which wouldn't be self-reliant anyway). But either way the functionality you are requesting isn't possible with that app.

Before looking at 3rd party apps, you could use Calendar instead. If you didn't sleep until the alarm, you could simply delete that day's event and be done with it. Snooze should still be functional. But all the rest of your calendar alerts would be set with the same terrible ringer and you would miss it entirely if you forgot to deactivate the silence switch on the side of your phone. 

After that, I suggest an app like MotionX Sleeptracker (24/7) or SleepCycle. They both work well for alarms and have some nice features that go along. That said, they may not work for you as you do have to start the "recording" every night. I find the process easy, but perhaps you wouldn't prefer it. 

So then it comes down to going through the App Store looking for a full-featured alarm clock. I've used several but never could get away from MotionX so I didn't stay long and I don't remember enough to know if they had the ability that you described.