I've used electric netting, not electric fence.
@Howard E is an expert on electric fencing.
Electric netting is not reliable in snow. I asked the manufacturer about that but did not get into why. They quickly said netting is not reliable. With electric fencing it is going to depend on how it is configured.
For any electricity to work as a deterrent the critter has to complete the circuit. With netting and some fencing the earth is the ground so the critter has to touch a hot part of the wiring and the earth. If you are putting strands of electric wiring on some wire mesh but insulating the electrical part from the strands the wire mesh may be the ground, depending on how it is hooked up. Or you might run ground and hot wires in a manner that the critter will touch both of those. Lots of different ways to configure it.
If you have a dry snow and are depending on the earth as a ground, the dry snow can insulate the critter from the earth so the circuit cannot be completed. No shock, no deterrent. If you have a snow wet enough to conduct a current and that snow is in contact with a hot wire then it can be shorted out and not work. It is OK for the snow to touch a ground wire as long as it is not touching a hot wire and the critter can still complete the circuit.
That does not mean that electrical is totally worthless in snow as long as it was in place and working before the snow. When a critter is shocked a time or two it learns to not challenge that fencing, whether it is hot or not. So the fencing tends to keep them away. The problem with that is that you always have the risk of a critter showing up that has not yet been shocked. When there is snow on the ground most wild critters are not weaning babies and sending them out to search for new hunting territory but new ones can still show up. And dogs can show up at any time. That is why it is not reliable.
Do you have a specific configuration in mind? We may be able to help. Or you can call the manufacturer and chat with them about how to set it up.