I've found turfs to work quite well in snow...I use chains because my drive is quite long and steep and we get ice storms on occasion. If you have no appreciable slope, I bet you'll do fine without chains ...is your tractor 4wd? Do you have a FEL on the front? can you lift your tractor with it ...if so, front chains are easy to install if you get into trouble and cheaper than rears ...If you are comfortable with the purchase, I would get them and hold in reserve. Four link ladder chains will work fine on your turfs (although the ride will not be as comfortable as two-link ladders.) and make sure you have chain tensioners.
As for what the chains do to blacktop ...same as they would on a car or truck; does your neighbor use them on his/her vehicle, ever?
But, I am betting you won't need them with your blower and relatively flat drives. As far as 2-3 foot storms, since you are blowing and not pushing (plowing) the depth matters relatively little, just take it easy (I'm hoping you have HST, otherwise, blowers are hard on clutches in big storms as is the pack-down that the plows leave at the end of your drive.