The charges would depend on the price plan you're on. If you're in a country where your domestic messaging allowance is included there wouldn't be extra charges, otherwise international messaging rates would apply for each message your phone received (whether opened or not)
We certainly hope you're traveling for good reasons. Deloused is right, texting charges would depend on the plan. You can confirm how you're being billed based on your plan and the country you're visiting using our Trip Planner Tool at this link http://vz.to/2cFFtj1 . It'll provide you with the information based on the plan you currently have.
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