Step 1:

Go to Settings -> Filters -> Create a new filter

Step 2:

Type the following into "Has the words" field:

category:promotions older_than:90d

or 

before:2011/01/15

Step 3:

Click "Create filter with this search"

Step 4:

Select "Delete it" and Check the box labeled "Also apply filter to [...] matching conversations."

finally click "Create filter" button... 

And... we're done!

The key here is older_than:90d, you can just as easily create whatever time-based filter you want with that.  Additionally, the reverse of that filter is newer_than:90d

So, for example, using the same steps as above, we can create a Gmail filter that puts emails newer than 90 days under a specific label/folder...  Not sure exactly how this would benefit someone but I'm sure someone will find a use for the filter "newer_than:Xd"