I have tried several times to download the last skyrim trainer, when I unpack and open the folder there is no trainer just a read me note.
I just downloaded the Skyrim Trainer of March 20, 2013 and had no problems.
From the Troubleshooting Guide:
Solution 1:
Temporarily disable/uninstall all antivirus, firewall and other security software including browser addons and extensions. Some security products such as AVast contain browser extensions that can block the trainer downloads even though the primary product has been disabled.
Solution 2:
Try a different web browser.