How can I use a command to delete all files in Downloads whose dates added are greater than 1 year?
It's a relatively simple command to delete files within a directory greater than one year.  For instance, the following command executed in Terminal

find ~/Downloads/ -type f -mtime +365 -exec rm {} \;

will delete all files in the ~/Downloads directory older than one year.


find is the command that searches for "stuff"
-type f tells find what to look for, in this case files
-mtime +365 tells find that the modified time should be greater than 365 days
-exec rm {} passes (executes) each "found" item to the command rm


What I like to do is test it out by excluding the -exec rm {} \; portion and make sure I am getting the correct results.  Once I am certain, I just add it in to complete the remove.

One Caveat!!  These files are not added to your "Trash."  The command  bypasses the Trash and are immediately deleted, so use with caution.


A Safer Way...

(Thanks to user lucasoldaini in the comments below)

If you want to move your files to the "Trash", simply replace the -exec rm {} \; portion to -exec mv {} ~/.Trash \;

They will remain in your Trash until the next time you empty it.

You can get more information on each command by viewing their man pages: 


man find
man exec