I'll probably just wrap the entire back of the card with a <div id='back'> tag.

As a more concrete example, let's say the front template of the card is something like this:

<div class="kanji" lang="ja">
    <p class="kanji-stroke-order" lang="ja">{{kanji}}</p>
</div>

The template for the back of the card would be:

<div class="backside">
  {{FrontSide}}

  <!-- Rest of the back template -->
</div>

And the CSS would be something like:

.kanji {
  padding: 1em;
}

.backside .kanji {
  padding: 0;
}

That is, by adding a backside class you can make sure that you can add the different CSS styling you want.