No. If she is comfortable in short sleeves at home in the winter, I don't see why she wouldn't be at daycare. You could also send her with a cardigan or hoodie in case she gets cold. I like to do a zipper hoodie because then it is more like a jacket and I won't get judged for sending him in the same one every day.
I think short-sleeves should be fine; as others have said, you can just leave a hoodie or something in the room, just in case. Our daycare is usually pretty warm in the winter anyway.
We live in a warmer climate but my son wore long sleeves ONCE last year. We just sent him with a jacket everyday. All those cute shirts I bought unworn