Offer her rehab, not a hotel in my opinion. If she says no then she isn't ready to get well and I am pretty sure there are 24 hr. Wal-Mart's, laundromats, diners, a bus syation, an airport, a train station etc where she can go to warm up. She may even be able to catch some winks in a chair. I lived by O Hare Airport and the homeless snuck in and often holed up for hours without being caught.
The discomfort they put up with not to get help is mind boggling.
Gentle hugs.