Most of the time the answer is no.
Many web hosting providers also supply software that you can use from the web browser you already have! Beginners can incorporate fairly advanced features, such as multimedia and forms that require CGI (common gateway interface) scripts -- things that used to require hiring a programmer or other specialist.
Some web browser programs provide the ability to compose your own web pages and upload them to your site.
Proprietary web design programs, such as Dreamweaver® or FrontPage®, can be used to make visually stunning pages, but can be expensive and have a fairly steep learning curve. So, unless you already own them and feel comfortable using them, they may not make life easer for you.
A major caveat though is that many of the proprietary web design programs add extra coding to control appearance that increases overhead and can adversely affect performance of your web site.
In fact, HTML was designed to be easy to use and universally available, requiring only a text editor, included on most personal computers and servers. Many of the most visited web pages were made with a text editor!
Lately (after 2008) I have been advising most clients to adopt Open Source CMS (Content Management Systems) such as WordPress on their hosting. The free CMS sites such as Google/Blogger, WordPress.com, Facebook Pages, etc. are another good option -- most will let you use your own domain name as well.