According to the Syrian Observatory for Human Rights, the army shelled Jizeh and the west of Atman village in the southern province of Daraa.
Battles raged on in several parts of Daraa, pitting rebels and a local Al-Qaeda affiliate against Hezbollah and their Iranian and Syrian allies, said the Observatory.
"Despite the fighting, the Hezbollah-led advance was forced to slow down by heavy snow in the area," said Observatory director Rami Abdel Rahman.
The reports come on the fifth day of a major Hezbollah-led offensive in the southern provinces of Daraa and Quneitra, as well as the west of Damascus province.
Signup to our newsletter and follow us on Facebook and Twitter!
The area is important because of its proximity to Jordan, Damascus and the Israeli-occupied Golan Heights.
In recent days, pro-regime troops have seized a string of villages and strategic hilltops that rebels and the Al-Qaeda-affiliated Al-Nusra Front had been holding for around a year.
This week, for the first time in Syria's war, state television acknowledged that President Bashar al-Assad's army is fighting alongside Hezbollah and Iranian officers in its bid to crush a nearly four-year rebellion.
The Observatory's Abdel Rahman told AFP on Thursday that 300 elite Hezbollah fighters are deployed on Syria's southern front.
"This really is Hezbollah's battle," he said.
On January 18, six Hezbollah fighters and an Iranian general were killed in an Israeli air strike in Quneitra.