What will be the effect of drinking cold drinks to the pregnant woman like me?

It's "urban legend". There is no proven "effect" of cold drinks on pregnant women or their baby.

None different than if you weren't pregnant.

My doctor told me that if I haven't felt the baby move then I need to drink some cold juice or cold water or eat ice and it will usually make the baby move

Please do not eat ice during pregnancy. Why? It can cause dehydration.

In the end, drinking cold drinks during pregnancy does not do anything harmful to you or baby. Indulge yourself as long as there is no alcohol in those cold drinks.