Winter Cycling - Suspension frame for winter?

I put some studded tires on an old schwinn hybrid bike, and rode around in snow and ice with confidence. Old Man Winter ain't so bad! But I have found that riding on sidewalks and bike paths that have had foot traffic on them is a bit of a rattling, vibrating, and jarring experience. I am considering finding a bike with some suspension? Ideally it would take 700c tires, so that I could transfer over my current fender, studded tires, and perhaps use my current wheelset on the schwinn as a spare set for quick changes. Then maybe turn the old schwinn frame into something else in the future, or put it at the curb for scavengers.

Would having some suspension make that much of a difference ?

Without adjustable coil or air shocks, it's likely that the suspension will stiffen up enough to be ineffective in the cold. Elastomer shocks and non-adjustable oil-damped shocks will basically lock themselves out.

In other words, unless you're game to commit some $$$ to the project, it probably won't work.

I ride a 700c suspension MTB bike in the winter, but it isn't something I'd leave locked up outside all day.