The 250 tire kit will make the bike harder to lean over and obviously this will effect your lean angle and so forth. As for the winterizing I keep my bikes in a heated garage and I start them regularly and run them, and when the weather allows I take a little ride. Before I had the heated garage though I used to shut off the gas at the tank and run the bike till it runs out of gas and also drain the carbs (on my FJ1200 carbed bike) I remove the battery and put it on a trickle charger. I know people who will go so far as to fog there engine before they put it away.
To be honest I've had no trouble at all covering my bike over the winter and puttin in the battery every once in a while and running it. Others may think different but I have had zero issues doing this. Keep the battery charged in a warm place it'll last four or five seasons.
Good luck and welcome to zx forums