I just meant that it's easy to add chlorine to the water when it's not frozen. If you don't mind chipping/boring a hole to get access to the water, that's fine, but if you add chlorine and there is no circulation, it can settle to the bottom of the pool as its denser than water until thoroughly mixed. If you have a vinyl pool, that might be a problem. With a plaster pool, it might be OK so long as you don't dump a bunch in quickly. If there is any way for you to very slowly pour some in and then use something to try and stir the water, then that would be good.
However, don't expect the chlorine to spread to other areas of the pool so you could get algae in those areas. Multiple chip/bore holes would be needed -- sounds like a lot of work which is why I made the "when it's not frozen" comment.
So long as you treat your pool as soon as the ice thaws and before the water warms up, then you can easily kill any algae that has formed. That's what most people do as part of spring opening. Getting rid of a small amount of algae is no big deal.
Richard