Blogging software, like Blogger and Wordpress, almost always allow it. But they usually make you put it in a special box. This is not usually a hard feature to find.
If your widget does not work, try this.
Put the "Standard" (not customization) widget into a page. View the page where you put it in your browser. Hit Control-U, or the Apple equivalent.
This will pop up a new web page showing you the HTML that's actual in your page. If you don't see the widget code that you put in, then your system does not allow it and took it out. If you do see it, look closely to make sure it is all there and has not been altered by some robot.
Best of luck,