"I couldn't believe it when Dad won the Daily Prophet Draw. Seven hundred galleons!"
--Ron Weasley, in his birthday letter to Harry (PA1)
The Daily Prophet runs a small article announcing the winner. In it we find out that the Weasleys will use the gold to travel to Egypt where Bill Weasley works as a curse breaker for Gringotts Bank. They will be in Egypt for a month, returning to England a week before term starts at Hogwarts. The article also features a picture of the entire Weasley family, including Ron’s pet rat Scabbers, in front of a pyramid.
While in Egypt, Ron writes to wish Harry a happy birthday. Also in the letter is the information that there is still enough gold left over for Ron’s parents to purchase him a new wand.
It says they are staying in Egypt for a month, returning to England a week before the term starts. Term starts Sept 1, a week before that is August 24, so we can assume they left July 24, 1993.
The actual drawing of Mr. Weasley's name therefore would have been shortly before July 24.
This event may seem unimportant at first, but we find out towards the end of Prisoner of Azkaban that it is the most important event of the third book. The picture that was featured in the Daily Prophet was what let Sirius Black know that Peter Pettigrew was still alive. This fact then fueled his need for revenge which gave him enough strength to break out of Azkaban.