There's an additional burden on their network, and they should be able to recoup some of that cost.
But almost every carrier I've seen would charge extortionate rates - hundreds or thousands of times the price they would charge their local customers for.
If they have no way to recoup the additional cost of all the incoming visitors, then they can't invest in expanding infrastructure.
It's probably a pretty limited scenario though.
Yesterday, that traffic typically was priced at euros per _mega_byte, starting at the first bit transferred; starting today that's at most €7.70 + VAT per _giga_byte, starting after you have used your (fairly generous) fair use allotment, going down to €2,50 per gigabyte in the coming years.
Naturally, countries who see many tourists heavily opposed this change and lobbied to keep the maximum price that the EU now has set high.
I have still to see a reason in this thread that justifies the higher prices. If connections between different companies in a country work without significant cost, why is different between (european) countries? Damn, most of the time are the same company! It's price gouging and a racket.