Is it possible to mount Ubuntu 10.10's partition on Windows 7?
You have a couple that can Read And/Or Write to Ext2 And/Or Ext3 And/Or Ext4 file systems and can mount this fyle systems in windows. Some are:
Ext2Read - http://sourceforge.net/projects/ext2read/files/ (Most updated)
Ext2fsd - http://www.ext2fsd.com/ (Second Most Updated)
Fs Driver - http://www.fs-driver.org/
Disk Internals (Linux Read) - http://www.diskinternals.com/linux-reader/ (Popular several years ago)
Explore2FS - http://www.chrysocome.net/explore2fs (Super Popular some years ago)
Now for the compatibility with Windows 7:
Ext2Read - Confirmed Windows 7
Now for the "problems" you should watch out.
Even though you can read and maybe write to linux files and directories from windows there has been several problems regarding the issue of reading/writing from windows to Linux via tools like this. For example:
Maybe others. Some small cases include loosing a lot of information. So this is a big warning if you want to use tools like this. Anyway if has been also tested by several people and to them it worked good. So it all depends on you.
The most reliable way to access Linux filesystems from Windows is to do it via a virtual machine. There are several options. CoLinux is the lightest one, but might be difficult to install (I don't think there's an up-to-date distribution, so if you want ext4 and btrfs you have to assemble the pieces), and I think CoLinux doesn't work on 64-bit Windows. Otherwise you can use a hosted virtual machine such as VirtualBox, see for example How to import existing Linux partition into VirtualBox as guest?.
The simple answer is "it's very tricky and not polished." assuming you're 10.10 is installed on ext4 (which I believe is the default). What you could do is mount your /home dir on a fat32 file system and that would allow you to mount it on the windows side. This should help some if you decided to go with that route. Remember to back up the data already in your /home dir before switching where the OS looks for it.