It is more about what the users need to get from the site than how big it is. If the site consists of 10 pages each of which is clearly linked in the home page, and the site is just giving information then it may not need a search.
If people will come to the site and want to find information that is not naturally available in the heirarchy then you should provide a search. Even a portfolio site MAY justify a search, if people will be coming to the site to find examples of types of your work, for example. If you have 20 pages and they are easy to scan through, then maybe not.
And a site that is selling products directly needs a search - if nothing else because it makes it look more professional, and can give an idea that there are more products than there actually are. If your site has changing information - changing in a way that does not involve a site rework - then you need a search.
So don't just consider the size. Consider the usage. If you have a small site, then providing a basic search is not a major overhead, and if it would make the user experience better, then do it. The other side is that if the user would be confused by a search, then don't provide it.
Many celebrity/personal sites do not include a search, because their structure is very basic - a menu of links, each of which link to another page with information on. They do not require a search because the amount of information is very limited, and the only reasonable route to accessing it is the menus. They are normally kept up to date with new links if there are new routes or pages. This is a case where, irrepective of the number of pages, the usability would not be enhanced with a search.