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I just got the App updated to 4.25 last night and added my Wall Connector. Here's a SS of it added to my Tesla App. Yes, I'm in the US. It's pretty barebones. There's an option to schedule charging times and that's about it.
Sorry - I can't answer you winter question, but I'd probably still buy the Mobile Connector regardless if you use the SC and don't plug in at home. It's just a good backup to have.
I have the Laminars - they are pretty good quality covers. As long as you like the look, don't think you'll have any issues. Of course - I think the Laminars look better. :P