At the moment it is unclear what you want Postgres to return. You say it should order by persons.updated_at but you do not retrieve that field from the database.
I think, what you want to do is:
SELECT date(updated_at), count(updated_at) as total_count
FROM "persons"
WHERE ("persons"."updated_at" BETWEEN '2012-10-17 00:00:00.000000' AND '2012-11-07 12:25:04.082224')
GROUP BY date(updated_at)
ORDER BY count(updated_at) DESC -- this line changed!
Now you are explicitly telling the DB to sort by the resulting value from the COUNT-aggregate. You could also use: ORDER BY 2 DESC, effectively telling the database to sort by the second column in the resultset. However I highly prefer explicitly stating the column for clarity.
Note that I’m currently unable to test this query, but I do think this should work.