We actively see owls arrive at various times throughout the day at both Hogwarts, as well as at peoples homes.
Examples of mail that arrived other times.
- Charlie Weasly in Sorcerers Stone (Midnight)
The clock on the wall had just chimed midnight when the portrait hole burst open. Ron appeared out of nowhere as he pulled off Harry's invisibility cloak. There was a tap on the dark window. "It's Hedwig!" said Harry, hurrying to let her in. "She'll have Charlie's answer!"
- Ministry of Magic Chamber of Secrets(approx 9-10 pm)
Aunt Petunia was just passing around a box of after-dinner mints when a huge barn owl swooped through the dining room window, dropped a letter on Mrs. Mason's head
- Hedwig - The Prisoner of Azkaban (1AM)
Silhouetted against the golden moon, and growing larger every moment, was a large, strangely lopsided creature, and it was flapping in Harry's direction.
Examples of official mail that arrives at breakfast.
- Hogwarts acceptance letters - Chamber of Secrets
Harry heard from Hogwarts one sunny morning about a week after he had arrived at the Burrow. "Letters from school," said Mr. Weasley, passing Harry and Ron identical envelopes of yellowish parchment, addressed in green ink. "Dumbledore already knows you're here, Harry - doesn't miss a trick, that man.
- Daily Prophet - Sorcerers Stone
The owl then fluttered onto the floor and began to attack Hagrid's coat. "Don't do that." Harry tried to wave the owl out of the way, but it snapped its beak fiercely at him and carried on savaging the coat."Hagrid!" said Harry loudly. "There's an owl "Pay him," Hagrid grunted into the sofa."What?""He wants payin' fer deliverin' the paper.
- Packages from mail order companies Sorcerers Stone
As the owls flooded into the Great Hall as usual, everyone's attention was caught at once by a long, thin package carried by six large screech owls.
So While it appears while typically official mail tends to arrive during the breakfast window, mail does not have a required time to arrive.