My daughter has a cold so she's taking the day off from preschool.
My daughter is not going to preschool today because she's sick with a cold.
この場合、次のように保育園に伝えるといいですよ。
ーMy daughter has a cold so she's taking the day off from preschool.
「娘は風邪をひいているので保育園を休ませます」
to take the day off from ... で「…を休む」と言えます。
to have a cold で「風邪をひいている」
ーMy daughter is not going to preschool today because she's sick with a cold.
「娘は風邪をひいたので、今日は保育園を休みます」
not going to preschool で「保育園に行かない」＝「休む」とも言えます。
to be sick with a cold で「風邪にかかっている」
ご参考まで！
カナダ 
