The lifecycle of Windows XP has nothing to do with its legal status. The product will be protected by copyright long after Microsoft has dropped support. However, this protection does not mean the software cannot be used without a license.
First of all, 'Can I use Windows without a license?' and 'Can I install Windows without a license' are two different questions. Let's start with the first.
Generally, yes, you may use software without a license. Microsoft may disagree, but has no absolute say in this. Copyright, by its nature, covers the copying and distribution of a work, not its use. Its use is not one of the exclusive rights the author has been granted and you do not need the author's permission (i.e. license) for this.
Likewise, you do not need a musician's consent to listen when his song plays in a restaurant and you don't need your own copy of a film when a friend invites you over to watch it.
Installing the operating system is a different matter. You are making a copy and you'll need the author's permission for that, but exceptions may apply if such a copy is required for the intended use. For instance, playing a CD will load chunks of music into an audio buffer, but does not constitute copyright infringement. Making such a copy without having a legitimate one to begin with, often does.
Note that while copyright is covered extensively through a number international treaties, no two countries are the same. The above explanation may differ from local copyright law. Besides, not everything you can or cannot do is directly governed by copyright law, however. You may be bound by terms of the license agreement, granting you rights you would not normally have, conditionally.
In short, end of support does not mean Windows XP is suddenly legally available for free, but the legal status of its use is all but trivial.