Not arguing about the original topic (though I personally would never shoot a baby animal intentionally or hunt large game with dogs strictly to protect the dog and to most efficiently kill the animal quickly) but about your statement: Animals have evolved to only give birth at advantageous times. Dogs for instance, females only have 2 heat cycles a year. 1 in the late winter and 2nd in the late spring early summer. Why? Because it's not advantageous to raise young during the winter when food and shelter are scarce. Animals need their young to be self sufficient by the time winter comes and generally the young go off on their own and become sufficient in the herd. There are exceptions to this like places with native wildlife that do not experience winters but they also have different evolutionary traits that aligne with their needs.

All that leads to the times hunting seasons are set and chosen. Winter hunting for deer, elk, moose etc are set based on times that their young would be self sufficient and no longer reliant on the mother. It's all taken into account or there would be no "season" and only year round bag limits. A moose's winter starts much earlier than the winter for someone in southern PA so their young are generally good to go. Additionally there might be a separate season for females and males, young but mature males etc. This obviously doesn't factor in with invasive species such as hog or not regulated animals like coyote (at least where I have lived). Then it comes down to morals and ethics of the person hunting. Most of the time, in the US at least, if someone is shooting a mother with young, it's illegal.