It’s not that cold. The climate sites lists an average December temperature range of 59 degrees high and 47 degrees low around Jerusalem. Rain starts in November and ends in March.
Israels climate and growing season isn’t comparable to the eastern US. They have a rainy and (really really) dry season. Grass grows when there’s rain, herd animals give birth with the new pasture, it’s as simple as that.
A simple search for Jerusalem or Bethlehem shows that this year for the week of Christmas the lows every night are in the low 30s. Now if you think grass grows at that temperature you’re kidding no one but yourself. Last week Jerusalem was virtually shut down because of a snow storm. Good grief.