Unless your phone does not support certain networks because of hardware that is not installed, because you bought the iPhone in a country where the local cellular networks use a different bandwidth to broadcast their signal, I can see no reason why the hardware should fail, crossing a border within Europe.
If your iPhone 7 is a model A1778, it should also support following carriers in Sweden:
3, Tele2, Telenor and Telia
as well as your local Austrian carriers:
3, A1 and T-mobile
(according to this article: http://www.apple.com/iphone/LTE/#iphone-7-iphone-7-plus)