After fixation of your cells with 4% (hopefully 'buffered') PFA-solution NOT ALL organic / inorganic substrata of your cells perhaps are "really fixed"(in terms of irreversible change of conformation of proteins, like using glutar-di-aldehyde for primary fixation, etc.). So you should inform about the task of your research experiment /processing - your IF-staining - a bit more in detail.
Usually (and IMHO) for IF-methods there should not be a very big difference in using PBS at room temperature...assuming you use the correct PBS (make, osmolarity) (:-)) but perhaps a literature search in depth for the matter would find some argument to do washing either with ice cold PBS or PBS at normal room temperature.
PS: the purpose of "washing fixed cells" first of all is (as the term "washing" = get rid of, cleaning normally implies) to get rid of (most probably otherwise disturbing) remnants of unreacted fixative and or byproducts of the fixation reaction itself.
Coming also to mind: additional 'blocking of free aldehydes' in a tissue section or fixed cell suspension, since such left aldehyde sites would interfere with (dye, staining) reactions after further processing....