Images in Webmail email signatures
You can write email signatures using only text or HTML. This last option is the one I recommend and you have it very easy since both Horde and Roundcube clients provide you with a text editor with which you can design your HTML signature.
In addition to text styles like bold, colors, underline, HTML allows you to display a image as part of your email signature.
Horde
In the case of Horde for a signature in HTML mode, locate the icon, as shown in the following image: