FYI, I sent in my first gen nano mid-November (received by Apple on 11/22).
I finally received notification of replacement on 12/17 and the replacement showed up today. As the serial number hinted at, it is a current (6th generation) 8GB nano, in silver. (My original was black.) Apple's website shows the warranty as expired, but see the text below.
Enclosed with the nano was a letter with the following text:
Dear Apple Customer:
Thank you for participating in the iPod nano (1st generation) Replacement Program. Please find your replacement iPod enclosed.
Serial Number
Please note that your replacement iPod has a serial number different to that of your original iPod nano. In some cases due to limited availability of replacement stock of iPod nano (1st generation) Apple may have replaced your iPod with a more recent iPod model of equivalent or better specification. Always retain a record of your serial number(s) for future reference.
Warranty
Your replacement iPod product is warranted to be free from defects for 90 days from the date of service.
To ensure that your iPod is up to date, download the latest iTunes from Apple's website at http://www.apple.com/itunes/download. Questions regarding the operation of your iPod can be answered at Apple's online support site at http://www.apple.com/support/ipod.
Sincerely,
AppleCare Service