There is no native functionality in Anaplan to populate Todays date. It can be achieved via a daily import driven via Anaplan connect however.
You will need to take a use input or the import from a schedule Anaplan connect action and use this to create a logic which will prevent writing into certain time periods.
If the data comes from another Anaplan model then you can simply filter out the dates. If it comes from an external source then I would use dynamic cell access and turn off write access into those dates.