Your formula is correct as long as the field with the date of birth is called DOB.
I would possibly modify it to this: If(DOB<=12/31/2017, :star: ,"") if you want to actually have a blank field when the condition does not hold instead of a field with a space.
Hope this helps!
Actually the original formula had several issues.
Emoji are characters and need to be enclosed in straight quotes.
Hardcoded date strings need to be enclosed in straight quotes. As written 12/31/2017 is a mathematical expression that evaluates to about 0.000191917091816.
It is also better to compare text strings with text strings rather than hoping that Airtable will correctly do data type conversion.
it is better to completely omit the third parameter than to include a text string of one space or an empty text string.