I know that they had sleigh rides here in Austria during Felicity's time, so I'm sure they'd have used them in the US too in areas where it snowed. Their sleighs might not have been as fancy as the once shown in the painting. Even during Kirsten's time they'd have sleighs during snow months, as the wheels get stuck more easily than vats.

Up in the mountains sleighs are still occassionally used in those areas were they can't use modern trucks etc.