I grew up on the west side of Cuyahoga County, and at the time, we had RWD cars (okay, one was a Corvair), never used snow tires, and never had problems.
Those used to driving in heavy snow can get by without winter tires.
Those new to frozen delight would certainly be safer on winter tires.
Finally, I put a set of Blizzaks on the older Accord for the winter, and the difference is such that I will consider buying more of them for the other cars for next winter.
For someone moving to the north from Florida, I would absolutely recommend a set of winter tires.