Open the list in Infopath 2010 for editing.
Add a new variable, e.g. Today.
Add a new Form Load rule and assign the variable to the current date and time. This will be used for checking the date later.
Add a button to the form.
To make it simple, I only enable submission if the button is clicked. The default Save button is disabled by going to Form Options.
Add a Formatting rule to the form and disable it if the date falls outside of the preferred date range.
Finally, link the button to a Form Submit action.
