PHP has already a long history behind him : Legendary PHP 1.0, PHP/FI, PHP 3.0 and PHP 4.0.
PHP 4 was designed to be as compatible with earlier versions of PHP as possible and very little functionality was broken in the process. If you're really unsure about compatibility you should install PHP 4 in a test environment and run your scripts there.
Also see the appropriate migration appendix of this manual.
Although native session support didn't exist in PHP 3, there are third-party applications that did (and still do) offer session functionality. The most common method was by using PHPLIB.