Hot air balloons can go up in the rain.
But since rain poses risks to the hot air balloon pilot and any passengers a hot air balloon pilot will not take a hot air balloon up in the rain.
However if the hot air balloon is already in the air and the rain begins while the hot air balloon is in the air then the pilot can safely fly the hot air balloon and will land it.
The safest time to fly a hot air balloon is when the rain is not coming down and the weather is nice and clear without much wind.
All professional hot air balloon pilots will not fly in really high winds or rain especially during heavy rain or if a thunderstorm is forecast.