We (72 and 75) kayaked on a Seabourn cruise to Greenland. Three years ago we kayaked on the Antarctic peninsula.
Yes, the cruise line provided dry suits.
The kayaking was in very still water - protected coves with ripples, no waves - some photogenic small bits of floating ice. We felt very confident - our local river kayaking (New Jersey) is technically more challenging.
A guide in a kayak led the group of passengers, and a zodiac boat stayed close to the group, presumably to rescue anybody who got into trouble. I wouldn't want to fall in, but I felt safe.
It was quiet and peaceful - almost a moment of solitude even though we were part of a group.
Note, on the same trip Seabourn sponsored a "polar plunge" for passengers (tethered to the ship by a cable) who wanted to jump off the tender platform into the arctic water - in their bathing suits. Seems insane to me, but a couple of participants actually lingered in the water for maybe 30 seconds.