I'm not sure I can provide much advise for the vulva area, but for the paws this is the best advice I can give:
Musher's Secret Paw Wax
We go through a can of this every winter and it works wonders. My guy has had issues with the same thing you're describing-- redness and inflammation on the feet as a result of contact with the snow. Booties will definitely help, too, but my dog hates wearing them and unless he's running on ice we just use the wax and he's fine.
In the interim, keep her feet dry, and if you have any coconut oil, you can rub that on them to help with any bacteria.