The date format that you can enter to perform a date search should not matter. In my testing with my date type columns I was able to search with the dd/mm/yyyy format without issue. What are you experiencing?
It might be possible to search on just the year portion, it would be a little custom though. It would be tricky if the user can enter a full date or the year, if they are only selecting a year then it would be a bit easier. Using a select list for the years would be best for this.