You attempted to pass the DateTime.MinValue, 1/1/0001 12:00:00 AM, which is a common technique. You discovered, however, that SQL Server datetime type does not like dates prior 1753.
DateTime is a structure and cannot be null. However, a nullable version is available. You can declare it like so...
DateTime? anullableDateTime;
If the .AddNote method has a nullable DateTime parameter, you are all set. Just set a null like so...
txtCommentDateCreateNote.Text != string.Empty ? DateTime.Parse(txtCommentDateCreateNote.Text) : null
If not, decide on a minimum date you will treat as null in your UI. 1/1/1900 is a favorite, and do this...
txtCommentDateCreateNote.Text != string.Empty ? DateTime.Parse(txtCommentDateCreateNote.Text) : new DateTime(1900,1,1)
Just set your textbox.Text = null when you retrieve this value. Saving a real date has the added advantage of not having to deal with nulls in your database queries.