Windows will be flawed for vulnerabilities no matter what other platforms connect to it.
A well patched distro of Linux with firewall is a very secure environment!!!
A properly secured Windows system is no less secure them a properly secured Linux system. The main reason Windows machines are easier to compromise is because they aren't properly hardened.
By the same token, an Ill-maintained Linux box is no more difficult to break into then a Ill maintained windows machine; in fact, if the person in question is more skilled with Linux it may very well be easier, after all, despite everybody's claims to the contrary, hackers don't memorize every single vulnerability, and like anybody else they will choose the path of least resistance. The thing is this is always a windows machine.
Perhaps the company has a forgotten router sitting in some dormant corner of their facility, and it just happens to be in the gateways DMZ. This exposes it directly to the internet. Now let's say said router is using an outdated Linux version. A experienced Linux "hacker" will have a far easier time breaking in through that entryway then trying to get into any of the many windows machines that aren't within the DMZ.
Some people make the (incorrect, but let's humour them for now) analogy that Windows is a piece of sugar glass and Linux is a piece of bulletproof glass. And then they ask which one we would rather have protecting us if we were shot at. The problem here is that the ideal case is
not be shot at at all, as well as the fact that the way many linux systems and their companion windows systems are setup,
your not behind the analogical bulletproof glass.