I have the most recent version of Ubuntu in Virtualbox on Windows 7 host. How secure will that be? I mean if I get malware on windows how will that affect the Ubuntu system I am working on?
The host has complete control over the guest. So if there is malware running on the host, the guest is compromised as well.
In practice, most malware out there only tries to infect common software, such as the OS itself, web browsers, media players, etc. Virtual machines are such a rare case that malware authors typically don't bother, especially given that the diversity of systems that could be running inside the VM means a lot of work for the malware author.
However, this may change as virtual machines become more common. For example copy-paste would make a relatively simple infection vector (you think you're copying some innocent text into the VM but the malware makes you in fact paste a command that opens the gates; also, consider that by spying the host clipboard, the malware has access to anything you copy-paste even from within the VM to within the VM). And if you're the victim of a targeted attack rather than some common malware, all bets are off.
If you have a network link between the host and the guest, the malware may attempt propagate that way, like it would to any other machine in your local network.
First you need to define what you mean by "security". If you are talking about the normal Windows problems of "Malware" and "Virusus", this should not be a significant area of concern. For all practical purposes you can treat the virtual guest like a separate machine with the same security concerns as another entity on the network. Malware is typically platform dependent and passing from one OS to another is not only difficult in theory but incredibly rare in practice.
It is true that the host has control over the guest including ability to intercept and inject packets on it's network interface, but to my knowledge no known malware currently exists to target this case.
If you are talking about the kinds of security involves protection against targeted attacks ... people looking at what's available on your system and using any surface available, your security is only as strong as it's weakest link. In this case you would render your activities in Ubuntu only as secure or private as the host Windows system was. If it was compromised, the guest would not be safe from various forms of spying and attack. The network interface could be eaves dropped on, the hard disk could be read from the image file outside the VM, and so on.
It should also be mentioned that since the Virtual Machine receives keyboard input from and displays graphics on host devices, that automated malware that can capture keyboard input and/or screenshots could potentially steal entered and displayed information (passwords, etc). This wouldn't require a targeted attack.