Getting the bar and chain wet isn't going to do it any harm, as long as you get it dry before you put the saw away. After getting it wet, make sure you run it for a while so things get warm, drive off the water and oil things up again. If thats not possible I would take the bar and chain off when I got home and dry and oil it manually.
You might want to consider using biodegradable bar oil so the oil slick you leave in the water isn't too toxic. Although some people say that just water will lube the bar well enough if it's partly submerged. Personally I would go with a vege based oil. Then you are are OK sawing normally as well and have an out if you are challenged about creating an oil slick
Obviously keep the powerhead dry, but if you do slip up and drown one the general procedure is to drain the tanks, remove the spark plug, pull it over to get all the water out and get it started again ASAP and run it till it's warm, dry and oily again.
Water shouldn't kill your saws, but leaving them wet will encourage corrosion, bearing damage and general bad things.
Cheers
Ian