During a fresh load of the game, the characters you create will start 1st of Hearthfire 12:00 Noon. If you choose "Drop to Dos" and restart the game, this is a fresh start. If you create a new character before loading any other saves, your new character will start 1st of Hearthfire 12:00 Noon
If you have already loaded a character and choose "New Game", the character you create will start 1st Morning Star 12:00 Midnight.
This is true for ver 1.06 and 1.07. (Although the Anthology version is technically 1.06 it was also tested and verified.)
This is NOT true for ver 1.03. In this version all new characters, created fresh, or created using the "New Game" option will always start 1st Hearthfire 12:00 Noon. (Information I've read so far, seems to indicate that 1.03 is the earliest retail release of the game, but I'm not certain.)
In the DEMO version (pre Feb 1994) you cannot create characters, however the date is also 1st of Hearthfire 12:00 Noon.
So having a start date of 1st Morning Star, appears to be a bug that was introduced somewhere between versions 1.04-1.06.
(EDIT: My guess is 1.05. From the patch notes; "New characters created from within the game will work". Version 1.03 seems to work fine, so I bet something broke in 1.04 and the fix in 1.05 added the Morning Star bug.)
EDIT: I was able to obtain patches for 1.01, 1.04, and 1.05. From all accounts I can find, there is no 1.02 patch and 1.03 is the primary retail version. This is why you can't find .02 and .03. This makes sense, but need someone to check who actually owns an original retail copy.
Ver 1.01 patch. It isn't a true test, but I tried to use it to upgrade the DEMO and downgrade Ver 1.03. The DEMO wouldn't load. The downgraded ver 1.03 operated the same with the exception of not giving the version number on exit. "Operated the same": meaning that saving from a fresh start or after creating a new character from "New Game" both start the game on 1st Hearthfire.
Ver 1.04 patch. Patch notes from ver 1.05 state; "New characters created from within the game will work". Using Patch 1.04 on the 1.03 game, I could still create characters in both manners. I wasn't able to determine what needed to be fixed for version 1.05. The fix isn't specific so it could be something in the stats creation or something you discover later. My focus was on the start dates. Version 1.04 creates characters in both manners starting on 1st Hearthfire.
Ver 1.05 patch. I applied this patch directly to the Ver 1.03 game. It operates the same as 1.06 and 1.07. Whatever 1.05 fixed in the character creation from within the game for version 1.04, it added the "Morning Star" bug for all future versions.
::Now I want to know more about this from the 1.04 patch: "Multiple 'Fortify' on a single spell now fortify all stats that are in the spell. Therefore a spell that fortifies STR, INT, and WIL will now fortify all those stats rather than changing your gender, for example. It will NOT fix your gender if you're already changed. (sorry)"

