It's absolutely fine to use thin warm layers in a car seat. You do not need to do anything extreme in terms of stripping her down to her clothes, and re-dressing her at your destination. Some people choose to go this route, and that's fine, but there ARE safe winter wear alternatives that can be worn in a car seat.
Your baby is 1? If so, you're golden. Toddlerhood is when it's easy. It's when they're school age and needing winter wear for recess and the trip to/from school when things get complicated (and rather annoying, IME
).
Start with an undershirt (ie: onesie) and then layer a long sleeved shirt overtop. Add pants (I love fleece and lined pants/jeans), and use warm socks on her feet. From there you can add a layer of fleece. I far prefer a one-piece fleece to a two-piece anything when it comes to an infant or young toddler. It's easier and you don't get the bulk of a coat stopping right at the hips where straps should be laying tight against the body. My personal fave is the MEC Ursus suit, but a very close second is the one-piece by Columbia. Last year I was lucky enough to find a one-piece fleece by Columbia that also offered an optional zip off wind breaker for overtop. The wind breaker portion was extremely thin and so I felt fine adding it as an additional layer on the coldest of days.
Add a hat, cover her hands, and use Stonz over Robeez lined boots (or not, but it's my personal fave combo), and quite honestly she will be snug as a bug.
It's ok to loosen her car seat straps a *little bit* to accomodate one layer of fleece. You want to make sure you get the harness nice and snug once she's buckled. The issue with winter wear is compressibility, which really isn't an issue with fleece. Use common sense, and keep the harness very snug, and use as little clothing as needed to stay warm enough that particular outing.
Once she's buckled in and tightened you can add a blanket on her lap.
Hope that helps.