I think it may be the way you are implimenting it.
It appears that you are trying to add this to your theme as individual files however I do not see anywhere in the code you provided where you are calling on the searchform.php file in the theme itself.
As such I tested the code you provided and was able to successfully get it to work on my custom theme by adjusting the location of where I placed the code snippets you provided.
Here was my steps.
First I placed searchform.php code into the header.php file of my theme.
<div class="search-field">
</div>
<form role="search" method="get" class="search-form" action="<?php echo home_url( "https://wordpress.stackexchange.com/" ); ?>">
<label for="search-input" id="search-label" class="search-label">
Search for:
</label>
<input id="search-input" type="search" class="search-input" placeholder="Search …" value="" name="s" title="Search for:" />
<input type="submit" class="search-submit" value="Search" />
</form>
Next I placed search.js into the footer.php file of my theme by adding the script tag around it and adding it right before the closing tag.
<script>
document.getElementById("search-label").addEventListener("click", function(e) {
if (e.target == this) {
e.preventDefault();
this.classList.toggle("clicked");
}
});
</script>
After that I added your function to functions.php of the custom theme
function searchfunction() {
wp_enqueue_script( 'my-script', get_stylesheet_directory_uri() . '/js/search.js', array( 'jquery' ) );
}
add_action( 'wp_enqueue_scripts', 'searchfunction' );
Finally I added your css style to themes stylesheet.
#ht-masthead .search-field {
background-color: transparent;
background-image: url(images/search-icon.png);
background-position: 5px center;
background-repeat: no-repeat;
background-size: 24px 24px;
border: none;
cursor: pointer;
height: 37px;
margin: 3px 0;
padding: 0 0 0 34px;
position: relative;
-webkit-transition: width 400ms ease, background 400ms ease;
transition: width 400ms ease, background 400ms ease;
width: 230px;
}
#ht-masthead .search-field:focus {
background-color: #fff;
border: 2px solid #c3c0ab;
cursor: text;
outline: 0;
}
#ht-masthead .search-form {
display: none;
position: absolute;
right: 200px;
top: 200px;
}
.search-toggle:hover #ht-masthead .search-form {
display: block;
}
.search-form
.search-submit {
display: none;
}
.search-form {
position: relative;
}
.search-form label {
position: relative;
background: url('https://cdn4.iconfinder.com/data/icons/ionicons/512/icon-ios7-search-strong-128.png') 0 0 no-repeat;
background-size: cover;
width: 50px; height: 50px;
text-indent: 9999px;
overflow: hidden;
white-space: nowrap;
}
.search-input {
transform: translateY(-100%);
opacity: 0;
position: absolute;
top: 100%;
transition: opacity .25s, transform .25s;
left: 0;
z-index: -1;
border: 0;
outline: 0;
}
.search-label, .search-input {
background: #ccc;
padding: .5em;
display: inline-block;
}
.clicked + .search-input {
opacity: 1;
transform: translateY(0);
}
When I load the page I can see the same functionality as on your jsfiddle example you provided. I did notice with my theme, due to me having the header utilizing a high number z-index that it was hiding behind my header when it initially opened. However it is loading up on the site correctly.
Try this solution out and I hope it suits your needs.