Here we go, tried to make it easy and spelled out for everyone to grasp completely. I also attached the code in a text file so you could save it and reference later easily.
Code:
<p>What is today's date smarty? <b>{$smarty.now|date_format:$config.Appearance.date_format}</b></p>
<p>What month is it smarty? <b>{$smarty.now|date_format:"%B"}</b></p>
<p>What day of the month is it smarty? <b>{$smarty.now|date_format:"%e"}</b></p>
<p>What day of the week is it smarty? <b>{$smarty.now|date_format:"%A"}</b></p>
<p>What year is it smarty? <b>{$smarty.now|date_format:"%Y"}</b></p>
<p>Is it November smarty? <b>{if $smarty.now|date_format:"%B" eq "November"}Yes{else}No{/if}</b></p>
<p>Is it December smarty? <b>{if $smarty.now|date_format:"%B" eq "December"}Yes{else}No{/if}</b></p>
<p>Is it November 1st-9th smarty? <b>{if $smarty.now|date_format:"%B" eq "November" and $smarty.now|date_format:"%e" gte 1 and $smarty.now|date_format:"%e" lte 9}Yes{else}No{/if}</b></p>
<p>Is it November 10th-20th smarty? <b>{if $smarty.now|date_format:"%B" eq "November" and $smarty.now|date_format:"%e" gte 10 and $smarty.now|date_format:"%e" lte 20}Yes{else}No{/if}</b></p>
<p>Is it December 2nd-10th smarty? <b>{if $smarty.now|date_format:"%B" eq "December" and $smarty.now|date_format:"%e" gte 2 and $smarty.now|date_format:"%e" lte 10}Yes{else}No{/if}</b></p>
Output:
What is today's date smarty? 11-12-2013
What month is it smarty? November
What day of the month is it smarty? 12
What day of the week is it smarty? Tuesday
What year is it smarty? 2013
Is it November smarty? Yes
Is it December smarty? No
Is it November 1st-9th smarty? No
Is it November 10th-20th smarty? Yes
Is it December 2nd-10th smarty? No