We have had the same problem--my daughter has long, extremely narrow feet. She didn't start walking until she was 16 months old, and there still weren't any sandals in Stride Rite that would fit her. (They only had one shoe that was narrow enough for her foot, period.)
We've had good luck with some See Kai Run, but only a very few models that we could get snug at the ankle. If that ankle could get a secure fit, the wide toe box was no problem. Their Jayden model was great, and Qwynn (maybe discontinued now, not sure) and Sadie also fit her well. Their other shoes don't get as snug on her tiny ankle, so the whole shoe would just swim on her foot.
Jayden was our everyday shoe for her last fall & winter, and we had a pair of Ecco boots (they are labelled for "first walkers," the ones she had were a soft cherry red leather) that were also great and very flexible. They were not exactly snow boots (we grabbed some Lands End boots for actual snow play, but they were pretty stiff) but they were good shoes for cold weather and a good fit. She wore them a lot--anytime red would go with her clothes--and we'd use the Jaydens if she needed the more neutral brown. The Eccos were a very nice fit for her little foot.
Maybe check Zappos, online? I've never ordered there, but I've heard that they offer free return shipping, so if a shoe doesn't fit, you know it won't cost more to return it...
It might be worthwhile to have some thicker Ragg-wool type socks for her. (Hanna Andersson has some woolies for kids, and I'm sure they're around other places.)
I found that my daughter didn't do a lot of walking outside in snow her first walking-winter (she started walking in July at 16 months and the following winter, she did play in the snow some but wasn't really walking in "bad weather" a lot. We'd still carry her out to the car, etc.) This year (she's 2.5) I definitely had to get her a snow boot that is a flexible toddler shoe as well, because I know she'll be in and out a lot and really PLAYING out there on the hill.
I think Robeez makes more of an all-weather type of shoe or boot, don't they? Something meant for snow/rain. I can't swear to it, but that kind of thing might be your best bet if she's a new walker. Good luck!!