So do coal fired power plants use cooling towers?
Yes, many do.
Any plant that uses hot water as a medium will have some means of coolin and recirculating water. Coal plants might ALSO have a stack for dumping the crap that burned coal turns into and some use the same tower as a combined cooling tower and stack.
Some plants just dump hot waste water into a nearby Ocean, but you can't do that without heating up the area, unless you're in an area that can handle it (a natural lake biosphere certainly couldn't).
Some plants use dedicated ponds for this, rather than towers, but it's not very common, because you need pretty big artificial ponds and they aren't super awesome environmentally, as far as I am aware.