Good question!

I think its best to not water before 10 AM. Even though the water is warmer than the air it evaporates which cools things off. When temperatures are a little above freezing this extra cooling will create frost and even icicles. The ice will form the most aggresively as soon as the sprinklers go off (no more warm water being sprayed). I've witnessed this first hand.

I changed our sprinklers to water at 1:00 pm. once a week, for 25 minutes- the grass sections are turned off. Everything seems to do well with that amount of water and that frequency. I do have some pots and smaller gardens that I hand water between the sprinkler watering, if I see they look dry. Sometimes if there has been a wind and the air is dry, they can dry out very quickly. If it looks like rain or is raining, I try to turn them off, but sometimes it looks like rain, but doesn't. Then I just set them to water the next day, rain or no rain predicted.
If a frost is predicted, my hubby gets home at 3:30 and will run all the sprinklers for about 10 minutes. This helps if there is going to be a freeze or frost.

HTH
Susie