Not sure what part of the country you are from but once you get some seat time in your kayak you will feel more at ease about cold water kayak fishing. Just like anytime while on the water you need to watch what you are doing at all times. I keep a good dry pack with a change of cloths, first ad kit, fire starter and cook stove. Also try to keep your phone in a dry box.
I have not been out on the kayak in a few weeks but it has more to do with muddy lakes than cold. You can have some of the best fishing days of the year in the winter months and I hope you can get on the water sometime soon. It has just become cold here so we have a long while before warm up.