You need to tell it to select the option that's value is equal to that of $open_season_date ($date in my example)
i.e.
$date = 2; // or whatever
echo "<select name=\"date\">";
echo "<option value=\"1\""; if($date == 1) echo "selected"; echo ">Jan</option>";
echo "<option value=\"2\""; if($date == 2) echo "selected"; echo ">Feb</option>";
echo "</select>";
I assume your a newbie, so I will share a tip with you.
Don't leave double or single quotes out of your code. Forgetting them causes errors, corrupt data, or invalid data.
i.e.
<option value=1> should be <option value="1">