There is no 100% secure way to network your computer to an untrusted network, and there is no single measure which will provide near invulnerability. Security is not a bolt-on you should keep it in mind when you do anything.
If you have no firewall, and are not behind a NAT router, other internet users can and probably will try to connect to your computer. There are always bots scanning the net, especially in cable and DSL IP ranges.
Don't run un-necessary services. Don't run a web server you don't need, FTP server, ssh server and so on. You can find out which programs are listening for connections like this (run this command as root or with sudo):
You will probably have some results there. Understand what they are, and if you don't need them, turn them off, or set them up so they only respond to your local machine or IPs on your local (home) network.
If you are behind a NAT router, make sure uPNP is turned off if don't use it. Also, make sure port forwarding it set up so that only incoming traffic which you absolutely need to forwarded to your computer. Port forwarding is often called "virtual servers" in domestic routers.
It's a good idea to check what ports are open on your machine using a web based service such as shields up.
There is no magic bullet - you have to be part of the process and guard against risky behaviour.
Linux has a better track record than Windows when it comes to security, but it is not a perfectly secure system. The reasons for Window's bad record are numerous and some of them controversial. I don't think this is a good place to have that discussion.
On the specific question about whether someone can access your Windows partition when you use Linux... Do you share this partition using samba or some other network file system technology? If so, you need to make sure it is only accessible from machines which should have access to it and that the connection requires authentication. Take both
of these precautions, not just one of them.