A great stroller cover is not just great in the rain and snow, it actually creates a beautifully warm green house type atmosphere for your baby!! My little ones were chronic sock / shoe / hat / glove tossers, so a rain cover on super cold days was essential. Our favorite brand is Manito (see my full review here), because it's made of a nice waterproof nylon with plastic windows that zip open and shut, meaning you can take your kids in and out of the stroller without having to remove the cover, and you can also zip it open to hand them a snack, when you're move indoors, or if the kids are getting too warm (picture that love scene in "Titanic" - it can get quite toasty and actually steam up the windows in that rain cover LOL). They have single (in alpha & plus for strollers where the back reclines such as City Mini & G-Luxe, and beta for strollers where the seat is reversible and rotates via lever, such as UppaBaby Cruz & Vista ) and twin (for side by side strollers).
Mittens or gloves that are toddler proof? SNOWSTOPPERS!! They go all the way up to the elbow (under the jacket), so they keep snow out and toddlers can't pull them off, hurrah!!! SnowStoppers also make great super tall snow boots. Check out my full review of both the mittens and boots here.
Whether they just have a runny nose from the cold, their first cold, RSV, the flu, or allergies, you need to invest in a good nasal aspirator! My personal favorite is BabyVac - it hooks up to your vacuum hose - valves control the suction power so it gets out all the buggies but isn't painful or dangerous, and don't worry, the boogers get trapped in the small device and don't go into your vacuum. See my full review here! Others prefer Nose Frida, which is powered by your own mouth. You'll also need saline drops, to make sure it's super moist and easy to suction. Suctioning right after a steamy bath can help, too.
If baby wearing, you'll want to get a baby wearing coat or baby carrier cover. They'll make life easier. If just wearing here and there you can simply throw a pair of tights and leg warmers under kiddo's pants, or put them in a snow suit, or wrap a long warm blanket around you and the carrier. Jolly Jumper Snuggle Cover is probably the cheapest of the covers, and seems to be quite popular, though I've never tried it myself.
And I'll leave you with my final tip for surviving winter with littles. This is especially for stroller-pushing city-dwellers. Those corners after a snow storm? They can be a DOOZY!!! First, you need a nice stroller with decent sized wheels (that handy umbrella stroller you have? yeah right, put it away til spring). To get over the snow mounds, the trick is pulling the stroller BACKWARDS. Yep. You'll look a fool but it's the only way. Good luck out there, parents!!!