Keep your head and your toes warm, and you're good to go. A warm hat and mitts are essential, and good, waterproof boots (nothing worse than cold, wet feet.) Sorels are good, but I prefer Kamik (I have 1/2 dozen pairs of Kamik boots) and Baffins are good too.
As for a jacket, I find if my head and feet are warm, that when I am out hiking the dogs half the time I end up unzipping my jacket and taking my scarf and mitts off (unless it is windy, then I complain non-stop). I guess it depends on what type of walks you plan on taking....casual strolls through the neighborhood you will need a warmer jacket than if you plan to be out hiking on tough terrain where you will be building up a sweat.
Which brings me to layering -- what you wear under your jacket will make a huge difference. Get yourself some performance fleece and you will be super warm -- dress in plain old cotton and you will have a chill in no time.
I use snowshoes after the snow falls to remake our trails, then just walk in boots once we have packed a trail back down. Again it depends on what type of walking you will be doing -- if you plan to be out in the woods, get yourself some snow shoes.
For the dogs, I trim the hair on their feet back to avoid snowballs, but bag-balm on for the same reason, and leave their nails longer in the winter for better grip in the snow and ice. I do not use booties.
