The following CSS snippet will display your Emoji characters correctly in all browsers running on Windows, including Internet Explorer and Google Chrome.

.emojiText {
    font-family: "Segoe MDL2 Assets", "Segoe UI Symbol";
}

Then apply the CSS style to your text:

<p>
    Websites are funnier with emojis/emoticons:
    <span class="emojiText">&#128565; &#128126;</span>
</p>

Example:

😵 👾 🐙 🍪 ✊ 👍 🐢 👎 🚩 ☁ ✉ 🔨 ✈ 🌎

Unicode Private Use Area (PUA) example:

             