People have been throwing snowballs full of stones at cars and houses causing damage.
Gwent Police said it was investigating reports of people concealing stones inside snowballs before lobbing them at properties and vehicles in Blackwood.
Officers are appealing for people to hand over the names of perpetrators and are promising to fine those who are responsible.
Calling the incidents "disappointing", the force said it was investigating.
In a statement on Tuesday morning, it said: "Disappointed this morning to find reports of snowballs with stones in being thrown at houses and cars. Criminal damage is being investigated.
"Blackwood officers will get names, issue fines and offenders brought in.
"Residents, please report incidents live and give us names."
On Sunday, Gwent Police received "multiple reports" of youths throwing snowballs at moving vehicles in Newport and called the behaviour "dangerous and would not be tolerated".
A spokesman for the force warned people not to put others in danger "for your entertainment".
Meanwhile, in Bridgend, a woman injured in a road was pelted with snowballs by a group of 25-30 youths as police came to her aid.
Parts of Wales saw up to 10cm of snow over the weekend and a weather warning for ice lasted until Monday morning.
