I am not a TLS expert, but it is my understanding that basically nothing is going to happen when this certificate expires. This cert is what microsoft signs stuff with (for example, new updates, drivers...). There aren't any new updates being made for any SHA-1 system anyway.
The reason you canot connect to HTTPS sites when you change the date is because you are changing the date, not any significance pertaining to what that date is.
Firefox-based browsers do not rely on windows for encryption anyway. Chrome (at least on XP) partially does. but even for chrome and IE, nothing is going to change.