I like April because the days are usually warmish, even when "cold" it still isn't that cold, and when the sun comes out it is very warm. If I wait until May around here then generally everything is mud and mush, there is no firm or dry ground. Things dry up in June around here but then the black flies get so bad that the cows won't hardly stand still long enough to nurse. Also by then they are on pasture farther from home so you have to worry about wolves and cougars getting newborns....
I don't "baby" my animals by any means they are out in a field with some brush and trees for protection and rolled out hay to lay on. Had my first calf born last night and it was 16* and windy all night, I didn't worry one bit about her. Keep good mothering cows and breed some thick hair into them so they can survive the elements and let them be.