The phrases in your example
any other time of the year
any other time during the year
any other time throughout the year
are all equivalent, meaning other times than the present in a typical year. A possible subtlety is since you are using the idiomatic phrase
(this) time of the year
people may immediately think of the holiday season, not just that it's an arbitrary date during the year, this may be due to the Andy Williams Christmas anthem
It's the Most Wonderful Time Of The Year
In your example you might want to rephrase
you have a lot more chance
to
You have a better chance to get a girlfriend than any other time of the year.