How do electric vechicles hold up in something like this?
Not well, the heater is a major drain. If you stop the heater, the batteries get cold and perform significantly worse.
While you are right about “not well”, the other option can often be “not at all”
The batteries used in most EV’s should always work to some degree, with regards to temperatures experienced on Earth - the batteries & other systems in most ICE can be completely crippled/not work at all under certain temps faced on Earth
Now, you can specifically go out of your way to ruggedize all systems in your ICE so it works to a much better degree than the EV, but the average person is definitely not doing that.