If you are talking about cutting off electricity in winter, it will be for what are considered non-essential services, as for example hospitals must have a continuous supply of electricity.
In the US, there are pretty strict regulations about hospitals having back up generators or other sources of power in the even of power outages. Most critical equipment such as ventilators and infusion pumps have their own built in batteries, but for complex power hungry equipment these batteries might only last 30 minutes. Not to mention the chaos of being in the middle of a surgery when all the lights and electrical operating tools stop working. I imagine there would be similar regulations in the EU.
But yes, you make a good point. In the scenario of planned power cuts, then governments might start placing limits on what you are and are not allowed to use electricity for. Good luck enforcing that, though.
It is worth mentioning that China banned bitcoin mining because they were also facing an energy crisis and it didn't solve a thing considering the fact that China's electricity usage continued growing like before, it didn't even have a small drop!
It's almost like bitcoin mining is completely inconsequential! Not to mention that in China a large proportion was using excess energy from hydropower which was otherwise being wasted during periods of low demand.