Alot of variables depend on leaving her overnight. First is the temp, which 45deg. is fine to hang deer in, so she should still be good tomorrow morning. The other thing is, how bad are the coyotes around there? If they are thick like they are here, you may not have any meat left by the time you get there tomorrow morning.
I'd wait 4 hrs from the time of the hit and go tracking, very quietly, very cautiously, and with as little light as possible. The moon is half full tonight so that will help.
Good Luck and let us know how it turns out.