I don’t know about when it is actually grown today in modern Israel, but, based only on Torah texts, Rashi on Genesis 8:22 says that winter is called “חֹרֶף” in Hebrew, because it is “the time for sowing barley and beans, which are early (חֲרִיפִין) to ripen quickly. The winter period is [the latter] half of Shevat, Adar, and half of Nissan.” The midpoint of the month of Shevat this year (2021) fell on January 28th.

The barley crop must be ripe by the second day of Passover (which was Monday, March 29th this year—2021), in order to bring the Omer offering in the Temple. If the Sages saw that the barley crop would not be ripe in time, they would declare an extra month to the year and make it a leap year.

“Similarly, if the court sees that [the barley crop] has not ripened, but that it is late in sprouting, or that the fruit trees that usually bloom at the time of the Pesach holiday have not bloomed, these two factors are sufficient,9 and the year is made full, even though the vernal equinox will fall before the sixteenth of Nisan.10

[The reason the year is] made full [because of these factors] is so that there will be [an abundant quantity] of ripened [barley] accessible, so that the wave offering of the omer can be brought from it on the sixteenth of Nisan,11 and so that the fruits will bloom, as they always do in the spring.”

(Rambam, Laws of Sanctifying the New Moon, 4:3)

L'orzo viene coltivato per tre mesi e matura presto: i suoi semi sono pronti per essere mangiati in primavera. In Israele oggi, l'orzo viene coltivato principalmente per il foraggio, e la maggior parte dei campi d'orzo del paese si trova nel Negev.