Yoshi crying to go outside but is too cold to do her business

I know there are a few cold weather threads but she is begging to go I outside despite crying when we're out there. I couldn't find a similar situation. I've tried everything, boots, no boots, taking her to her favorite spots by carrying her (sometimes carrying her wrapped in a blanket). There's about two feet of snow here in Chicago and the current temp is -15 F with wind chills making it feel -40 F. She's been peeing ok but she hasn't gone number two in 36+ hours. She's very particular and needs to find the right scent before going and every time we get outside she sniffs and then gets too cold to do anything. I've dug out a few spots but it doesn't seem to be working and now it's 1 am and she's howling to be let out but every time we bundle up and go out she won't go. And then we come back inside which she seems happy to do and then 5 minutes later she's by the door howling to go back out. I just don't know what to do.

[mod edit: changed category]