Someone might correct me, but I believe it is only in Brazil south that “chimarrão” (how they call this drink) is drank like this, hot and shared.
In Argentina and Uruguay you drink it individually. You can share the recipient with the mate in it, but once you added a refill of hot water and took the first sip, you have to drink it until the end before returning.
And in Paraguay they drink the “tereré” with cold water.