We have a small server running Windows Server 2003 Enterprise Edition, SP2 that only has 12GB of HD space. The
C:\WINNT\SoftwareDistribution\Download\ folder is taking up over 1 GB of space.
Is it safe for me to delete the items in this folder?
That folder is where Windows stores Windows Updates. It is generally safe to delete its contents so long as you have no pending updates. That is, if you have not performed any recent updates or at least have made sure to reboot and complete any recent updates, then you can delete them.
May as well remove the whole SoftwareDistribution folder used by Windows Update Service. Open a command line with administrator privileges and run:
Check for updates (will take longer then normal as it rebuilds it's database) and make sure it's all working then if desired backup and delete the SoftwareDistribution.old folder. No reboot is necessary.
Instead of doing what the others are advising you, I think it is much better and safer to use the Disk Cleanup tool bundled with Windows.
You can use it to cleanup system files, including the Windows Update cache. It will make a better job than you and save some headaches in the long run.
Read the Extra Cleaning - Delete Unneeded System Files & Programs section in this tutorial: Free Up Wasted Space with Disk Cleanup.
You will see that Disk Cleanup can safely delete for you more than just the Windows Update cache. It can delete the Windows Defender cache, thumbnails, user history files, etc. And, most of all, it will do the deletion safely, in a way that won't cause issues afterwards.
It is a very useful tool and very much ignored by users.