So, after digging into Three.js examples, I found a way how to do this. http://learningthreejs.com/blog/2011/08/15/lets-do-a-sky/ is outdated. A way used in examples is to add skybox into second scene with fixed camera, and render both scenes. Look at webgl_materials_cars.html example.
Also because I use 3rd person camera assigned to character, I must get world rotation from character camera to skybox camera. This can be done on render with:
function render(){
<...>
skyboxCamera.rotation.setEulerFromRotationMatrix( new THREE.Matrix4().extractRotation( camera.matrixWorld ), skyboxCamera.eulerOrder );
renderer.render(skyboxScene, skyboxCamera);
renderer.render(scene, camera);
<...>
}