Dogs can handle it, except for rock salt. For you, get some good boots for walking - they exist (Saloman boots are super comfortable for me, but everyone is different!). Walking in the winter is the best (other than freezing rain), I find - quieter, less people, more calming. Then again, I have a lot of Scandinavian heritage ;)
I just hate clomping around in the boots. But I manage.
Now, do you have super-secret Scandinavian folk knowledge of good dog boots? Because I have tried, and he hates the damn things. And the rock salt irritates his feet quite a bit.
I'm not convinced that dog boots are ever necessary. Wild dogs can't afford shoes. Sled dogs run all day barefoot in sub-zero temperatures. I have four random little mutts between ten and twenty pounds, and even they rarely have trouble in the winter. I took one of them out for a run today at 15 deg. F, no problem.
Salt is a problem. If there's a lot of salt out, I'll rub a sealant into their pads before we go out. Lots of things will work -- lip balm or lanolin are my favorites, but petroleum jelly would probably do in a pinch. But whatever you use, the most important thing is to simply wash the salt out of their pads after they come back in. I've done this for almost a decade in Colorado and none of my dogs has ever had a cracked or frost-bitten pad.