Bummer... I was hoping maybe warmer. It’s miserably cold here, too. Warmer than last night. Tonight it’s only (supposedly) going down to -13. I guess we’ll see.
If you have a garage or storage area you could bring her into, you might talk your mom into that. If it’s somewhere she doesn’t have to look at or interact with the hen, she might be persuaded, especially if there’s a cage/kennel/etc. Just somewhere you could keep an eye on her and apply whatever medications folks have suggested that you can get hold of. People have these fears; you can seldom argue them out of them, even if you’re the one who’s afraid and trying to convince *yourself* not to be.
You might try grinding up some oatmeal and soaking it in a bit of warm water for several minutes until it gets gluey, then pack her wound with it. You probably have that, and I’ve read it can help to draw the “poison” (in this case probably dead white blood cells) out. It won’t hurt her, at any rate, and it might help reduce the inflammation.