Set your DateTime picker Properties:
myDateTimePicker.Format = DateTimePickerFormat.Custom;
myDateTimePicker.CustomFormat = "yyyy";
myDateTimePicker.ShowUpDown = true;
This allows the user to select the year only (you can add text such as "End of " to the custom format if you wish)
Then:
DateTime endOfYear = new DateTime(myDateTimePicker.Value.Year, 12, 31, 23, 59, 59);