According to TCM, barley water is a labour inducing food but I don't think that small quantities will cause any issues with pregnancy. Unless you have previous history of pre-term labour or any other complications then you should be careful with what you take in.
everything in moderation, dear! and don't go drinking like 3 cups a day... go with 1 cup a day or less and see if you feel any discomfort. stop if there is.
It won’t cause any contraction if u take in moderation or limited amounts. The same for other cooling stuff like pineapple and watermelon.
thanks