Hi again.
It's OK, the more questions you ask, the better off you and your flock will be.
Yesterday was a good time to start your coop! Seriously, you will come across many challenges that will slow your building progress. Brooding in the coop is by far best. If your brood is small, it takes longer to get gross, but the dust left on the walls from them is thick and gross. But work within your means and make it work for you.
The sooner you get chicks the sooner you get eggs. I won't get chicks later than April in the future. My June chicks are barely starting to lay and they will molt come fall. So instead of getting eggs for summer, fall, winter, spring. summer, fall, molt.... From those, I will only get spring, summer, fall, molt. Do you see the difference? All chickens will molt their second winter. My February born girls started laying around 4th of July.
Frozen ground creates special conditions I haven't had work with. But many coops are not anchored to the ground but built on stilts to allow for chickens to have extra rain cover. I guess it depends on how big you are going...
ETA: Don't forget windows for light and plenty of ventilation.