Is one part of the day more prevalent then other when it comes to mammal animals mating? Is there an aggregating study that has been done to see if these living beings in nature mate mostly during day or night?
Why would it evolve?
No research (that I can find) is consistent with specific time of day mating across many species. I can't think of any reason why even just a few quite different mammals (e.g. mice, bats, lions, whales, and humans) would all find a fitness benefit of mating at the same specific time of day and therefore it is highly unlikely to evolve. I would suggest that if there are consistent patterns they are no reason other than coincidence (correlation over causality).
For example, dawn and dusk peaks in activity...
I have no references to back this idea up but lets see how this goes. The majority of mammals will be awake around dawn and dusk because there is likely an over lap between nocturnal and diurnal species at these times. Given that mating (normally) requires the participants to be awake then this would be a time when more animals are awake it is therefore a more likely time for mating to occur. But, as I already mentioned it would purely be because of the increased numbers awake.
Simple statistical illustration of the dawn & dusk idea...
Imagine a raffle with 2000 winning tickets. You buy 1000 and put 500 hundred of these in a box called nocturnal and the other 500 go in a box called diurnal. The raffle is drawn 24 times (perhaps every hour). The first 14 times it is drawn you can win if the ticket is from the nocturnal box, the latter 14 times you can instead check the diurnal box. This means during the first 10 draws you have a 25% chance of winning, and likewise in the latter 10 hours, but in the middle 4 hours there is a 50% chance every draw.
This comes down to a simple statistical phenomenon, if you don't buy a ticket you can't win the raffle.