For outdoor shoots - the best time to schedule a shoot is first and foremost when we have good weather. If it is cold, windy and rainy, chances are it will be quite difficult to get great images. Why? Because we are all pretty miserable. Sure we can fake it and probably get by but it will not be my best work. This can also apply here in Texas when it gets 100+ degrees outside. If it looks like the weather is going to be bad let me know and I will look at it. We will then look at an alternate time to do the shoot if we have to. Sometimes, on shoots that have a deadline, we will even come up with a plan B schedule beforehand so we will switch to that quickly if the need arises. However, a 20% chance of rain DOES NOT constitute a reason to cancel a shoot. Yes, I had that happen.
If at all possible, I prefer to schedule things during the week. If it has to be a weekend, Sunday is preferred although Friday evening may work for some. I try to leave Saturdays open if at all possible for weddings or other events that sometimes pop up.
The most common time to schedule an outdoor shoot is starting 2-3 hours before sunset. The low sun is far less intense and harsh and it also can be used as a great background source of light for illuminating people from behind and giving us that touch of sunflare that can be beautiful in images. Keep in mind though that this caries by location. If we are shooting in an area surrounded by high buildings or high trees, the sun will be hidden potentially far earlier. Having enough light is very important to take a photo and although I often supplement or use flashes, it gives a different character to the shot.
Alternatively, in the hottest months of the summer, we can schedule EARLY in the morning. I'm not a morning person but its worth it not to deal with the killer heat.
IF you are late to a shoot, it can significantly impact the quality of the shoot as we may not have that critical best light for long. Yes, it is possible that we will nail it but some of the best shots come through trying different things and that just takes time. This is a creative process and we have to have time for it to happen.
If you have to have a shoot at a certain location during the brightest times of the day, be prepared for it to show in your images. I can compensate for that with various techniques and lighting but it will never look like an image taken in a good location at the right time of day.