First winter with my EV – range and tyre pressure

Just had my first cold snap with the car and the range drop is real, but what surprised me more was the low tyre pressure warning popping up twice already. I’m guessing that’s the cold air shrinking, but should I be topping them up more often in winter? Also, for those in proper cold climates – are winter tyres actually worth it on an EV? I know the weight and torque are different to a petrol car, but I’m not sure if the extra cost makes sense when I WFH most days. Keen to hear what others do to keep things efficient and safe this time of year. Any advice appreciated.