He wore a wool suit on the third of April.
He wore a wool suit on April 3rd.
He wore a wool suit on the 3rd of April.
He wore a wool suit on April 3. (this isn't wrong, but I would prefer writing "April 3rd" and I would read this as "April third" not "April three.")
If he decided to wear a wool suit in the middle of the summer, I would write:
He wore a wool suit on the Fourth of July.
But I would only capitalize "Fourth" because that day is a fairly significant US holiday that we refer to by the date. If it were almost any other day (e.g., third of April, twenty-fifth of December, first of January), I wouldn't capitalize the number.