When you said morning suit formal my mind went straight to the likes of Royal Ascot and weddings. And that dress looks like something you'd see there.
A (big shapeless) wool coat would look so wrong with a lovely dress like that. Depending on the time of year, you may not need a coat. If you really think you'll be cold I would go more with a jacket so you can show off the dress.
And definitely not boots, not for a formal event.
You need to be more specific with the event though.
Is it full on morning suit? Are the men wearing top hats and specific coloured waistcoats ? If they are, then yes to a hat. If not then it's really up to you.