Legally, you can't. Apple owns the rights to the app, so only they have the legal right to distribute it. If you have a backup of Snow Leopard you can access, you can just grab that version of TextEdit and replace the one in Lion. Though it's slightly more complicated than than.
You can use Terminal to delete the Lion version of TextEdit since the OS insists it cannot be deleted if you just drag it to the trash. You can also do a Get Info on Lion's version of TextEdit. Then click on the lock and enter your admin password so you can modify it. Change all permissions to Read/Write and close the box. You can then put it in the trash.
Make sure to put the SL version of TextEdit in your user account. Otherwise, when you do a Repair Permissions, it will destroy SL's TextEdit by trying to set its permission to where the OS thinks they should be for Lion. It's safe in your user account since a Repair Permissions doesn't do anything to any file or folder in user account. I made a folder named Applications in my user account and put the Snow Leopard version of TextEdit there. There's no need to tell the OS where to find it. All TextEdit documents will open in the old version automatically.