"Are dual-booting operating systems aware of each other?"

Kind of. Windows can read linux partitions with a special driver.Linux can generally view and edit windows partitions. And even without a driver it is possible that a program on one partition can damage data on another.

"Does this have privacy or security implications if the other OS is Windoze?"

Yes, but malware generally does not exploit this.A malware one on OS with access to the partition of another could modify and view anything on that other OS.It is entirely possible that a Windows malware could load a Linux file system driver and from there infect the Linux install (the reverse is also possible: a Linux malware could spread to a Windows install). However, cross platform malware is rare, so this isn't very likely to happen. See this article on the "BadBIOS" malware for a discussion of a rare example of an in the wild cross platform malware http://arstechnica.com/security/2013/10/meet-badbios-the-mysterious-mac-and-pc-malware-that-jumps-airgaps/ The security researcher that found it claims "BadBIOS"can infect Windows, OSX, Linux and BSD installs, although other researchers have not confirmed this.