Is this a bathroom plumbing vent or an exhaust fan that discharges through the roof vent. A plumbing vent must be long enough to stay above the snow line. Otherwise the snow could start melting and re-freeze clogging it.
If it is an exhaust vent with a low profile discharge termination or one that uses low profile roof vent, it sometimes freezes when buried under the snow, same situation as with the plumbing vent. If this is the case, install an extension so it terminates higher than the highest anticipated snow level in your area.
As for the toilets… self flushing is usually caused by a faulty Douglas valve / flush valve. When its seal deteriorates, it allows water to run constantly and occasionally activates flushing mechanism.
To make sure that is not holding properly, add some food coloring to the tank and after a few minutes check if the water inside the bowl has changed color. If it does, the valve might require replacement.